Attempting to understand the nature of space has always been a prime occupation for philosophers and scientists. Perhaps as a result of this considerable discussion, it is difficult to provide an uncontroversial and clear definition of the nature of space, except its physical definition (see below). This article looks at the way space is dealt with variously by physicists, mathematicians and philosophers, and ...

Including:

• Space - Physics and Space
• Space - Measurement
• Space - Astronomy and space
• Space - Mathematics and space
• Space - The philosophy of space
• Space - The psychology of space
• Space - Anxiety and space
• Space - Personal space
• Space - Use of space
• Space - Reference

Read more here: » Space: Encyclopedia - Space

See also:

Space, Space - Physics and Space, Space - Measurement, Space - Astronomy and space, Space - Mathematics and space, Space - The philosophy of space, Space - The psychology of space, Space - Anxiety and space, Space - Personal space, Space - Use of space, Space - Reference

Read more here: » Space: Encyclopedia II - Space - Mathematics and space

The definition of physical space in relation to ownership, in which space is seen as property, has long been an important issue. Whilst some cultures assert the rights of the individual in terms of ownership, other cultures will identify with a communal approach to land ownership. Spatial planning is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space can also impact on human and cultural behaviour, being an important factor in architecture, where it will impact on the design of bui ...

See also:

Space, Space - Physics and Space, Space - Measurement, Space - Astronomy and space, Space - Mathematics and space, Space - The philosophy of space, Space - The psychology of space, Space - Anxiety and space, Space - Personal space, Space - Use of space, Space - Reference

Read more here: » Space: Encyclopedia II - Space - Use of space

Space is one of the few fundamental quantities in physics meaning it can't be defined via other quantities because there is nothing more fundamental known at present. Thus, similar to the definition of other fundamental quantities (like time and mass), space is defined via measurement. Currently, the standard space interval, called a standard meter or simply meter, is defined as the distance traveled by light in a vacuum during a time i ...

See also:

Space, Space - Physics and Space, Space - Measurement, Space - Astronomy and space, Space - Mathematics and space, Space - The philosophy of space, Space - The psychology of space, Space - Anxiety and space, Space - Personal space, Space - Use of space, Space - Reference

Read more here: » Space: Encyclopedia II - Space - Physics and Space

In mathematics, a space is a set, with some particular properties and usually some additional structure. It is not a formally defined concept as such, but a generic name for a number of similar concepts, most of which generalize some abstract properties of the physical concept of space. In particular, a vector space and specifically a Euclidean space can be seen as generalizations of the concept of a Euclidean coordinate system. Important varieties of vector spaces with more imposed structure include Banach space and Hilbert space. Distance measurement is abstracted as the concept of metric space and volume measu ...

See also:

Space, Space - Mathematical spaces, Space - Physics and space, Space - Spatial measurement, Space - The philosophy of space, Space - Spaces in psychology

Read more here: » Space: Encyclopedia II - Space - Mathematical spaces

In classical mechanics, the configuration space is the space of possible positions that a physical system may attain, possibly subject to external constraints. The configuration space of a typical system has the structure of a manifold; for this reason it is also called the configuration manifold. For example, the configuration space of a single particle moving in ordinary Euclidean 3-space is just R3. For N particles the configuration space is R3N, or possibly the subspa ...

Read more here: » Configuration space: Encyclopedia - Configuration space

Cognitive space uses the analogy of location in two, three or higher dimentional space to describe and categorize the thoughts, memories and ideas. Each individual has his/her cognitive space, resulting in a unique categorization of their ideas. The dimensions of this cognitive space depend on information, training and finally on a person's awareness. All this depends globally from the cultural setting. The relationship between cognitive space and language has been investigated by Izchak Schlesinger (ISBN 9780521434362). He argues that case categories are ...

Read more here: » Cognitive space: Encyclopedia - Cognitive space

In mathematics, Banach spaces, named after Stefan Banach who studied them, are one of the central objects of study in functional analysis. Many of the infinite-dimensional function spaces studied in functional analysis are examples of Banach spaces. Banach space - Definition. Banach spaces are defined as complete normed vector spaces. This means that a Banach space is a vector space V over the real or complex numbers with a norm ||.|| such that every Cauchy sequence (with respect to the metric dIncluding:

• Banach space - Definition
• Banach space - Examples
• Banach space - Linear operators
• Banach space - Dual space
• Banach space - Relationship to Hilbert spaces
• Banach space - Derivatives
• Banach space - Generalizations
• Banach space - Literature

Read more here: » Banach space: Encyclopedia - Banach space

In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and uniform convergence. The conceptual difference between uniform and topological structures is that in a uniform space, you can formalize the idea that "x is as close to a as y is to b", while in a topological space you can only formalize "x ...

Including:

• Uniform space - History
• Uniform space - Definition
• Uniform space - Entourage definition
• Uniform space - Uniform cover definition
• Uniform space - Pseudometrics definition
• Uniform space - Intuition
• Uniform space - Examples
• Uniform space - Uniformly continuous functions
• Uniform space - Topology of uniform spaces
• Uniform space - Completeness

Read more here: » Uniform space: Encyclopedia - Uniform space

A space observatory is any instrument in outer space which is used for observation of distant planets, galaxies, and other outer space objects. Space observatory - Introduction. A large number of observatories have been launched into orbit, and most of them have greatly enhanced our knowledge of the cosmos. Performing astronomy from the Earth's surface is limited by the filtering and distortion of electromagnetic radiation due to the Earth's atmosphere. This makes it desirable to place astrononomical ...

Including:

• Space observatory - Introduction
• Space observatory - NASA's Great Observatories
• Space observatory - Other notable space observatories
• Space observatory - Future space observatories

Read more here: » Space observatory: Encyclopedia - Space observatory

In graph theory, certain vector spaces over the two-element field Z2 are associated with an undirected graph; this allows one to use the tools of linear algebra to study graphs. Let G be a finite simple undirected graph with edge set E. The power set of E becomes a Z2-vector space if we take the symmetric difference as addition. Every element of this vector space can be thought of as a linear combination of edges with coefficient from Z2. In yet another interpr ...

Including:

• Cycle space - The binary cycle space
• Cycle space - The integral cycle space
• Cycle space - The cycle space over a field or commutative ring

Read more here: » Cycle space: Encyclopedia - Cycle space

In mathematical analysis, a metric space M is said to be complete (or Cauchy) if every Cauchy sequence of points in M has a limit that is also in M. Intuitively, a space is complete if it "doesn't have any holes", if there aren't any "points missing". For instance, the rational numbers are not complete, because √2 is "missing" even though you can construct a Cauchy sequence of rational numbers that converge to it. (See the examples below.) It is always possible to "fill all the holes", leading to t ...

Including:

• Complete space - Examples
• Complete space - Some theorems
• Complete space - Completion
• Complete space - Topologically complete spaces
• Complete space - Generalisations

Read more here: » Complete space: Encyclopedia - Complete space

In topology and related branches of mathematics, a connected space is a topological space which cannot be written as the disjoint union of two or more nonempty spaces. Connectedness is one of the principal topological properties that is used to distinguish topological spaces. A stronger notion is that of a path-connected space, which is a space where any two points can be joined by a path. It is usually easy to think about what is not connected. A simple example would be a space consisting of two rectangles, each of whic ...

Including:

• Connected space - Formal definition
• Connected space - Examples
• Connected space - Path connectedness
• Connected space - Local connectedness
• Connected space - Theorems

Read more here: » Connected space: Encyclopedia - Connected space

In mathematics, a subset of Euclidean space Rn is called compact if it is closed and bounded. For example, in R, the closed unit interval [0, 1] is compact, but the set of integers Z is not (it is not bounded) and neither is the half-open interval [0, 1) (it is not closed). A more modern approach is to call a topological space compact if all its open covers have a finite subcover. The Heine–Borel theorem affirms that this coincides with ...

Including:

• Compact space - History and motivation
• Compact space - Definitions
• Compact space - Compactness of subsets of Rn
• Compact space - Compactness of topological spaces
• Compact space - Examples of compact spaces
• Compact space - Theorems
• Compact space - Other forms of compactness

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In mathematics, a topological space is zero-dimensional if its topological dimension is zero, or equivalently, if it has a base consisting of clopen sets. A zero-dimensional Hausdorff space is necessarily totally disconnected, but the converse fails. Zero-dimensional Polish spaces are a particularly convenient setting for descriptive set theory. Examples of such spaces include Cantor space and Baire space. Hausdorff zero-dimensional spaces are precisely the subspaces of topological powers 2I ...

Read more here: » Zero-dimensional space: Encyclopedia - Zero-dimensional space

A vector space (or linear space) is the basic object of study in the branch of mathematics called linear algebra. If one considers geometrical vectors, and the operations one can perform upon these vectors such as addition of vectors, scalar multiplication, with some natural constraints such as closure of these operations, associativity of these and combinations of these operations, and so on, we arrive at a description of a m ...

Including:

• Vector space - Formal definition
• Vector space - Elementary properties
• Vector space - Examples
• Vector space - Subspaces and bases
• Vector space - Linear transformations
• Vector space - Generalizations and additional structures

Read more here: » Vector space: Encyclopedia - Vector space

A color model is an abstract mathematical model describing the way colors can be represented as tuples of numbers, typically as three or four values or color components (e.g. RGB and CMYK are color models). However, a color model with no associated mapping function to an absolute color space is a more or less arbitrary color system with little connection to the requirements of any given application. Adding a certain mapping function between the color model and a certain reference color space results in a definite "footpr ...

Including:

• Color space - Understanding the concept
• Color space - Notes
• Color space - Color space density
• Color space - Partial list of color spaces
• Color space - Generic color models
• Color space - Commercial color spaces
• Color space - Special-purpose color spaces
• Color space - Obsolete color spaces

Read more here: » Color space: Encyclopedia - Color space

Space:

A three-dimensional something that extends without bounds in all directions (this week) and is the field of physical objects and events and their order and relationships.

(See also: Space, Pagan, Paganism, Pagan Dictionary)

Space Usually the universe as perceived by our physical senses. It is disputed whether space exists apart from objects or is a property of objects, and also whether it is objective or subjective. Such difficulties arise from our attempt to abstract extension from the reality of which it is an aspect, just as we attempt to abstract matter and energy. The physical basis of our universe appears under these three aspects, and the attempt to conceive each of the three as separate existences and to construct the universe out of them is to court contradiction and to proceed in the inverse order.

In most arguments about the nature of space, space is unconsciously assumed at the outset of the inquiry, so that the reasoning becomes viciously circular. Is space the ultimate residue left after we have removed everything conceivable? In that case how can we define it in terms of anything which is supposed to be derived from it? We must either leave it undefined, as a primary postulate, or else define it in terms of something which lies beyond the physical plane altogether.

Again, the question whether the dimensions belong to space or to material objects arises from a false separation between these two, so that we speak of objects being in space, just as we speak of life as being in matter. We think of space as an absence of matter, as we think of darkness as an absence of light, and silence as absence of sound; and having thus created vacuums we proceed to fill them. In the view of occultism it would be nearer the truth to say that light is the absence of darkness, sound the absence of silence, and matter a form of the presence of space; and this is true in the sense that those things which appear to us most real are derived from those which seem to us most unreal, because not immediately physically perceivable. In theosophy, space is the infinite, eternal background of Being, Being itself, the ever-lasting substratum of, as well as the presence of, the universe; its apparent vacuity is due only to its lack of physical qualities to which our senses respond, and also to its perfect unity and uniformity. Space is living, incomprehensibly conscious, and hence a divinity; it is the only real world, while our manifested world born from and in it is a mayavi (illusory) one.

Theosophy, regarding the physical universe as merely one of many planes of kosmos, applies the term space to a much larger range. Yet it has the same characteristic meaning in all its applications: it figures, for instance, as one aspect of the trinity of space, energy, matter which is equivalent to the primordial unity. The fundamental hypostases are all derivative from ever-enduring, frontierless space, and Be-ness is symbolized by space, which no mind can either exclude nor conceive, and motion. In this conception are combined abstract space, motion, and duration.

Space is symbolized by the circle; a central point denotes spiritual monadic activity arising within abstract space. It is equivalent to akasa or aether, water or the waters; Chaos as the spatial deeps. Sometimes space in its manifestation is represented as a serpent with seven heads or as the great sea or deep. Occasionally called aupapaduka (parentless), because it is primary and the source of all, it is spoken of both as mulaprakriti and as parabrahman. In its manifested aspect it is bright space, son of dark space, the former being the ray dropped into cosmic depths. Parent space is the eternal ever-present cause of all -- the incomprehensible divinity, whose invisible robes are the mystic root of all matter and of the universe. Space is called Mother before its cosmic activity, and Father-Mother at the first stage of reawakening of manifestation.

In this connection a very clear distinction is drawn between abstract space, the limitless, frontierless, beginningless, and endless encompasser, container of all the various manifested spaces, which as individuals appear from and in its fathomless womb; and these latter spaces which are its offspring and which are collectively and individually the spatial ranges comprised within the boundaries of any manifested universe, such as a galaxy or solar system. Thus, we have the boundless spatial All or abstract space, and the innumerable universe or limited spaces arising within it. The former is absolute infinity and eternity; the later are the innumerable, relative spaces or universe scattered over the fields of the Boundless, called the spawn of the Great Mother.

Physical space is said to have six directions, the four cardinal points plus the zenith and nadir; or eight directions given by the axes joining the opposite corners of a cube. The six and the eight combine in the cube and octahedron. Nothing in the definition of geometrical space excludes the possibility of other spatial constructions, coexistent with our space and interblended with it and with each other. This helps in understanding such matters as chains of globes -- which, when we attempt to represent them by drawn diagrams, seem so confusing and contradictory -- and the manner in which other planes of consciousness and of objectivity may be related to the physical.

(See also: Space, Mysticism, Mysticism Dictionary)

A Theosophical definition of Space :

Space

Our universe, as popularly supposed, consists of space and matter and energy; but in theosophy we say that space itself is both conscious and substantial. It is in fact the root of the other two, matter and energy, which are fundamentally one thing, and this one fundamental thing is SPACE  - their essential and also their instrumental cause as well as their substantial cause  - and this is the reality of being, the heart of things.

Our teaching is that there are many universes, not merely one, our own home-universe; therefore are there many spaces with a background of a perfectly incomprehensible greater SPACE inclosing all  - a space which is still more ethereal, tenuous, spiritual, yes, divine, than the space-matter that we know or rather conceive of, which in its lowest aspect manifests the grossness of physical matter of common human knowledge. Space, therefore, considered in the abstract, is BEING, filled full, so to say, with other entities and things, of which we see a small part  - globes innumerable, stars and planets, nebulae and comets.

But all these material bodies are but effectual products or results of the infinitudes of the invisible and inner causal realms  - by far the larger part of the spaces of Space. The space therefore of any one universe is an entity  - a god. Fundamentally and essentially it is a spiritual entity, a divine entity indeed, of which we see naught but what we humans call the material and energic aspect  - behind which is the causal life, the causal intelligence.

The word is likewise frequently used in theosophical philosophy to signify the frontierless infinitudes of the Boundless; and because it is the very esse of life-consciousness-substance, it is incomparably more than the mere "container" that it is so often supposed to be by Occidental philosophers. (See also Universe; Milky Way)

See also: Space, Mysticism, Body Mind and Soul)