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 ...

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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

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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

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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 ...

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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

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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 ...

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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 ...

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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 ...

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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 ...

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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

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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

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Space has a range of definitions. One view of space is that it is part of the fundamental structure of the universe, a set of dimensions in which objects are separated and located, have size and shape, and through which they can move. A contrasting view is that space is part of a fundamental abstract mathematical conceptual framework (together with time and number) within which we compare and quantify the distance between objects, their sizes, their shapes, and their speeds. In this view space does not refer to any kind of entity that is ...

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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

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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 ...

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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

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The way in which space is perceived is an area which psychologists first began to study in the middle of the 19th century, and it is now thought by those concerned with such studies to be a distinct branch within psychology. Psychologists analysing the perception of space are concerned with how recognition of an object's physical appearance or its interactions are perceived. Other, more specialised topics studied include amodal perception and object permanence. The perception of surroundings is important due to its necessary relevance ...

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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

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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 ...

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

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Space has a range of definitions. One view of space is that it is part of the fundamental structure of the universe, a set of dimensions in which objects are separated and located, have size and shape, and through which they can move. A contrasting view is that space is part of a fundamental abstract mathematical conceptual framework (together with time and number) within which we compare and quantify the distance between objects, their sizes, their shapes, and their speeds. I ...

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

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Space exploration - Argentinian Space Agency. The Argentina Space Agency, founded in 1996 is oriented to the development of Earth Observing satellites. It has developed several satellite missions including SAC-A, the failed mission SAC-B and the currently operating SAC-C Space exploration - Brazilian Space Agency. The Brazilian Space Agency, founded in 1994, directs one of the youngest space programs. Brazil's space program is the most advanced in South America. It suffered a m ...

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Space exploration, Space exploration - Orbiting and reaching space, Space exploration - Space agencies, Space exploration - Argentinian Space Agency, Space exploration - Brazilian Space Agency, Space exploration - Canadian Space Agency, Space exploration - China National Space Administration, Space exploration - European Space Agency, Space exploration - Federal Space Agency of Russian Federation, Space exploration - Indian Space Research Organisation, Space exploration - Japan Aerospace Exploration Agency, Space exploration - National Aeronautics and Space Administration United States, Space exploration - National Space Agency of Ukraine, Space exploration - Space and Upper Atmosphere Research Commission Pakistan, Space exploration - Criticisms, Space exploration - Timeline of space exploration, Space exploration - 1957-1975, Space exploration - post-1975, Space exploration - Reusable spacecraft, Space exploration - Unmanned missions, Space exploration - Animals in space, Space exploration - Humans in space, Space exploration - Recent and future developments, Space exploration - Other, Space exploration - External link

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From a spaceflight perspective, the definition of space usually used is that space begins 100 km (62 miles) above Earth's surface. The United States sometimes uses a 50 mile definition. (See boundary to space.) Achieving orbit is essential for going anywhere else, such as to the Moon or Mars. The first successful orbital launch was of the Soviet unmanned Sputnik I mission on October 4, 1957. This spectacular success led to an escalation of the American space program, and to an undeclared Space Race between the two superpowers. Soviet ...

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Space exploration, Space exploration - Orbiting and reaching space, Space exploration - Space agencies, Space exploration - Argentinian Space Agency, Space exploration - Brazilian Space Agency, Space exploration - Canadian Space Agency, Space exploration - China National Space Administration, Space exploration - European Space Agency, Space exploration - Federal Space Agency of Russian Federation, Space exploration - Indian Space Research Organisation, Space exploration - Japan Aerospace Exploration Agency, Space exploration - National Aeronautics and Space Administration United States, Space exploration - National Space Agency of Ukraine, Space exploration - Space and Upper Atmosphere Research Commission Pakistan, Space exploration - Criticisms, Space exploration - Timeline of space exploration, Space exploration - 1957-1975, Space exploration - post-1975, Space exploration - Reusable spacecraft, Space exploration - Unmanned missions, Space exploration - Animals in space, Space exploration - Humans in space, Space exploration - Recent and future developments, Space exploration - Other, Space exploration - External link

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As mentioned above, every Hilbert space is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if ||v||² = (v,v) for all v. The converse is not always true; not every Banach space is a Hilbert space. A necessary and sufficient condition for a Banach space V to be associated to an inner product (which will then necessarily make V into a Hilbert space) is the parallelogram identity: for all u and ...

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Banach space, 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

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Space exploration - 1957-1975. 1Project Vanguard was transferred from the NRL to NASA immediately before launch. 2 The Soviet Union had attempted an earlier rendezvous on August 12, 1962; However, Vostok 3 and Vostok 4 were only within five kilometers of one another, and were in different orbital planes. Pravda, however, did not mention this information and indicated that rendezvous had been accomp ...

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Space exploration, Space exploration - Orbiting and reaching space, Space exploration - Space agencies, Space exploration - Argentinian Space Agency, Space exploration - Brazilian Space Agency, Space exploration - Canadian Space Agency, Space exploration - China National Space Administration, Space exploration - European Space Agency, Space exploration - Federal Space Agency of Russian Federation, Space exploration - Indian Space Research Organisation, Space exploration - Japan Aerospace Exploration Agency, Space exploration - National Aeronautics and Space Administration United States, Space exploration - National Space Agency of Ukraine, Space exploration - Space and Upper Atmosphere Research Commission Pakistan, Space exploration - Criticisms, Space exploration - Timeline of space exploration, Space exploration - 1957-1975, Space exploration - post-1975, Space exploration - Reusable spacecraft, Space exploration - Unmanned missions, Space exploration - Animals in space, Space exploration - Humans in space, Space exploration - Recent and future developments, Space exploration - Other, Space exploration - External link

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The class of all pointed spaces forms a category Top• with basepoint preserving continuous maps as morphisms. Another way to think about this category is as the comma category, ({•} ↓ Top) where {•} is any one point space and Top is the category of topological spaces. (This is also called a coslice category denoted {•}/Top). Objects in this category are continuous maps {•} → X. Such morphisms can be thought of as picking out a basepoint in X. Morphisms in ({•} ↓ Top) are morphisms in ...

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Pointed space, Pointed space - Category of pointed spaces, Pointed space - Operations on pointed spaces

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If V is a Banach space and K is the underlying field (either the real or the complex numbers), then K is itself a Banach space (using the absolute value as norm) and we can define the dual space V′ as V′ = L(V, K), the space of continuous linear maps into K. This is again a Banach space (with the operator norm). It can be used to define a n ...

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Banach space, 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

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Because of channels in the outer membrane of the mitochondria, the content of the intermembrane space is similar to that of the content of the cytoplasm. As electrons move down the proteins in the electron transport chain, the electrons lose energy to bring H+ ions from the mitochondrial matrix into the intermembrane space. As a concentration gradient of hydrogen ions forms, a protein called ATP synthase harnesses the potential energy of these ions and starts chemiosmosis, where the H+ ions reenter the c ...

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Intermembrane space, Intermembrane space - Intermembrane Space of Mitochondria, Intermembrane space - Intermembrane Space of Chloroplast

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