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Spaces | A Wisdom Archive on Spaces | | Spaces A selection of articles related to Spaces | |
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spaces, Gaps
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| ARTICLES RELATED TO Spaces | | | |  Spaces: Encyclopedia II - Topological space - Classification of topological spacesTopological spaces can be broadly classified, up to homeomorphism, by their topological properties. A topological property is a property of spaces that is invariant under homeomorphisms. To prove that two spaces are not homeomorphic it is sufficient to find a topological property which is not shared by them. Examples of such properties include connectedness, compactness, and various separation axioms.
See t ...
See also:Topological space, Topological space - Definition, Topological space - Comparison of topologies, Topological space - Continuous functions, Topological space - Alternative definitions, Topological space - Examples of topological spaces, Topological space - Topological constructions, Topological space - Classification of topological spaces, Topological space - Topological spaces with algebraic structure, Topological space - Topological spaces with order structure Read more here: » Topological space: Encyclopedia II - Topological space - Classification of topological spaces |
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| | | | | Spaces: Encyclopedia II - Pitch space - Fibered pitch space In analogy with mathematical usage, we might call a modulatory space the base space, and another space over each point of it, giving the register, a fiber. This gives what might be called a fibered picture of pitch space.
Less well known is the fact that a fibered picture of pitch space can also be obtained where the base space is a chordal space. For instance, suppose 2^a 3^b 5^c is a five-limit interval. If the base space is a chordal space of triads, and if each fiber consists of the integers, we may represent the five-limit interv ...
See also:Pitch space, Pitch space - History of pitch space, Pitch space - Fibered pitch space, Pitch space - External link Read more here: » Pitch space: Encyclopedia II - Pitch space - Fibered pitch space |
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| | | | | Spaces: Encyclopedia II - Hilbert space - Definition Every inner product <.,.> on a real or complex vector space H gives rise to a norm ||.|| as follows:
We call H a Hilbert space if it is complete with respect to this norm. Completeness in this context means that every Cauchy sequence of elements of the space converges to an element in the space, in the sense that the norm of differences approaches zero. Every Hilbert space is th ...
See also:Hilbert space, Hilbert space - Introduction, Hilbert space - Definition, Hilbert space - Examples, Hilbert space - Euclidean spaces, Hilbert space - Sequence spaces, Hilbert space - Lebesgue spaces, Hilbert space - Sobolev spaces, Hilbert space - Operations on Hilbert spaces, Hilbert space - Bases, Hilbert space - Orthogonal complements and projections, Hilbert space - Reflexivity, Hilbert space - Bounded operators, Hilbert space - Unbounded operators Read more here: » Hilbert space: Encyclopedia II - Hilbert space - Definition |
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| | | | | Spaces: Encyclopedia II - Space and survival - Opportunities for space colonization Space colonies do not currently exist. There is a concern that the human species may lose its technological knowledge, use up required resources or become extinct before it colonizes space.
The author Sylvia Engdahl wrote about the "Critical Stage", a period of time when a civilization has both the technology to expand into space and the technology to destroy itself. Engdahl states that the human civilization is at a Critical Stage, but that the funding for space exploration and colonization is minuscule c ...
See also:Space and survival, Space and survival - Uses of space colonization, Space and survival - Barrier, Space and survival - Location and distance, Space and survival - Multiple locations, Space and survival - Opportunities for space colonization, Space and survival - Uses of space science, Space and survival - Near-Earth objects, Space and survival - Books, Space and survival - Television Read more here: » Space and survival: Encyclopedia II - Space and survival - Opportunities for space colonization |
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| | | | | Spaces: Encyclopedia II - Space and survival - Uses of space science The observation and study of space protects Earth. Space hazards can be seen in advance and acted against.
Space and survival - Near-Earth objects.
Near-Earth Objects (NEOs) are asteroids, comets and large meteoroids that come close to or collide with Earth. Spaceguard is a name for efforts to discover and study NEOs.
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See also:Space and survival, Space and survival - Uses of space colonization, Space and survival - Barrier, Space and survival - Location and distance, Space and survival - Multiple locations, Space and survival - Opportunities for space colonization, Space and survival - Uses of space science, Space and survival - Near-Earth objects, Space and survival - Books, Space and survival - Television Read more here: » Space and survival: Encyclopedia II - Space and survival - Uses of space science |
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| | | | | Spaces: Encyclopedia II - Space exploration - Criticisms It is more expensive to perform certain tasks in space with humans rather than by robots or machines. Humans need large spacecraft that contain provisions such as a hermetic and temperature controlled cabin, production of breathable air, food and drink storage, waste disposal, voice- and other communication systems, and safety features such as crew escape systems, medical facilities, etc. There is also the question of the security of the spacecraft as whole; losing a robot is nowhere near as dramatic as human loss, so overall safety of non-h ...
See also: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 Read more here: » Space exploration: Encyclopedia II - Space exploration - Criticisms |
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| | | | | Spaces: Encyclopedia II - Space Mountain - Space Mountain at Disneyland Space Mountain was closed at Disneyland in April of 2003, as the roller coaster inside the mountain was being replaced with a completely new coaster, similar to the original. It was built by Vekoma. The official reopening was scheduled for July 15, 2005 - two days before the park's fiftieth birthday, although as of July 1, 2005 the ride has been open to the general public (this is known as a soft opening).
After being seated in the car, riders are first brought to a control tower where they see one or two Disneyland cast members and t ...
See also:Space Mountain, Space Mountain - Space Mountain at Disneyland, Space Mountain - Space Mountain in 2005 Disneyland, Space Mountain - Disneyland attraction facts, Space Mountain - Space Mountain at the Magic Kingdom, Space Mountain - Magic Kingdom attraction facts, Space Mountain - Space Mountain at Tokyo Disneyland, Space Mountain - Space Mountain at Disneyland Paris, Space Mountain - Space Mountain at Hong Kong Disneyland Read more here: » Space Mountain: Encyclopedia II - Space Mountain - Space Mountain at Disneyland |
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| | | | | Spaces: Encyclopedia II - Space and survival - Uses of space colonization Extinction can be prevented by improving the physical barrier or increasing the distance between people and the potential extinction event. For example, people survive imminent explosions by being in a bunker or evacuating. Pandemics are controlled by putting exposed people in quarantine and moving healthy people away.
Space and survival - Barrier.
Life support systems that enable people to live in space may also allow them to survive hazardous events. For example, an infectious disease or biological weapo ...
See also:Space and survival, Space and survival - Uses of space colonization, Space and survival - Barrier, Space and survival - Location and distance, Space and survival - Multiple locations, Space and survival - Opportunities for space colonization, Space and survival - Uses of space science, Space and survival - Near-Earth objects, Space and survival - Books, Space and survival - Television Read more here: » Space and survival: Encyclopedia II - Space and survival - Uses of space colonization |
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| | | | | Spaces: Encyclopedia II - Uniform space - Topology of uniform spaces Every uniform space X becomes a topological space by defining a subset O of X to be open if and only if for every x in O there exists an entourage V such that V[x] is a subset of O. It is possible that two different uniform structures generate the same topology on X. The resulting topology is a symmetric topology; that is, the space is an R0-space.
Every uniform space is a completely regular topological space, and conversely, every completely regular space can be turned into a uniform space (often in many ways ...
See also:Uniform space, 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 II - Uniform space - Topology of uniform spaces |
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| | | | | | Spaces: Encyclopedia II - Space Race - The end of the Space Race While the Sputnik 1 launch can clearly be called the start of the Space Race, its end is more debatable. Most hotly contested during the 1960s, the Space Race continued apace through the Apollo moon landing of 1969. Although they followed Apollo 11 with five more manned lunar landings, American space scientists turned to new arenas. Skylab would gather data, and the Space Shuttle would work on returning spaceships intact from space journeys. Americans would claim that by first landing a man on the moon they had won this unofficial "race". So ...
See also:Space Race, Space Race - Historical background, Space Race - Early military influences, Space Race - German contributions, Space Race - Cold War roots of the Space Race, Space Race - Artificial satellites start the race, Space Race - Sputnik, Space Race - Satellite communications, Space Race - Other noteworthy satellites, Space Race - More Soviet successes: Living creatures in space, Space Race - Animals in space, Space Race - Humans in space, Space Race - Lunar missions, Space Race - Unmanned probes, Space Race - Landing a human on the moon, Space Race - Other successes, Space Race - Missions to other planets, Space Race - Launches and docking, Space Race - Military competition in space, Space Race - The end of the Space Race, Space Race - Organization funding and the economic impact, Space Race - Deaths, Space Race - Timeline 1957-1975, Space Race - Legacy of the Space Race, Space Race - Advances in technology and education, Space Race - More space races to come?, Space Race - Notes Read more here: » Space Race: Encyclopedia II - Space Race - The end of the Space Race |
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| | | | | Spaces: Encyclopedia II - Space station - Types of space station Broadly speaking, the space stations so far launched have been of two types; the earlier stations, Salyut and Skylab, have been "monolithic", intended to be constructed and launched in one piece, and then manned by a crew later. As such, they generally contained all their supplies and experimental equipment when launched, and were considered "expended", and then abandoned, when these were used up.
Starting with Salyut 6 and 7, a change was seen; these were built with two docking ports, which allowed a second crew to visit, bringing a ...
See also:Space station, Space station - Past and present space stations, Space station - Types of space station, Space station - List of occupied space stations with statistics, Space station - In fiction Read more here: » Space station: Encyclopedia II - Space station - Types of space station |
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| | | | | | Spaces: Encyclopedia II - Banach space - Examples Throughout, let K stand for one of the fields R or C.
The familiar Euclidean spaces Kn, where the Euclidean norm of x = (x1, ..., xn) is given by ||x|| = (∑ |xi|2)1/2, are Banach spaces.
The space of all continuous functions f : [a, b] → K defined on a closed interval [a, b] becomes a Banach space if we define the norm of such a f ...
See also: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 Read more here: » Banach space: Encyclopedia II - Banach space - Examples |
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| | | | | Spaces: Encyclopedia II - Hilbert space - Examples In these examples, we will assume the underlying field of scalars is C, although the definitions apply to the case in which the underlying field of scalars is R.
Hilbert space - Euclidean spaces.
Cn with the inner product definition
where the bar over a complex number denotes its complex conjugate.
Hilbert space - Sequence spaces.
Much more typical are the infinite dimensional Hilbert spaces however. If B is any set, we define the sequence space little l2 over ...
See also:Hilbert space, Hilbert space - Introduction, Hilbert space - Definition, Hilbert space - Examples, Hilbert space - Euclidean spaces, Hilbert space - Sequence spaces, Hilbert space - Lebesgue spaces, Hilbert space - Sobolev spaces, Hilbert space - Operations on Hilbert spaces, Hilbert space - Bases, Hilbert space - Orthogonal complements and projections, Hilbert space - Reflexivity, Hilbert space - Bounded operators, Hilbert space - Unbounded operators Read more here: » Hilbert space: Encyclopedia II - Hilbert space - Examples |
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| | | | | Spaces: Encyclopedia II - Space Race - Legacy of the Space Race
Space Race - Advances in technology and education.
Technology, especially in aerospace engineering and electronic communication, advanced greatly during this period. The effects of the Space Race however went far beyond rocketry, physics, and astronomy. "Space age technology" extended to fields as diverse as home economics and forest defoliation studies, and the push to win the race c ...
See also:Space Race, Space Race - Historical background, Space Race - Early military influences, Space Race - German contributions, Space Race - Cold War roots of the Space Race, Space Race - Artificial satellites start the race, Space Race - Sputnik, Space Race - Satellite communications, Space Race - Other noteworthy satellites, Space Race - More Soviet successes: Living creatures in space, Space Race - Animals in space, Space Race - Humans in space, Space Race - Lunar missions, Space Race - Unmanned probes, Space Race - Landing a human on the moon, Space Race - Other successes, Space Race - Missions to other planets, Space Race - Launches and docking, Space Race - Military competition in space, Space Race - The end of the Space Race, Space Race - Organization funding and the economic impact, Space Race - Deaths, Space Race - Timeline 1957-1975, Space Race - Legacy of the Space Race, Space Race - Advances in technology and education, Space Race - More space races to come?, Space Race - Notes Read more here: » Space Race: Encyclopedia II - Space Race - Legacy of the Space Race |
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| | | | | | Spaces: Encyclopedia II - Space Race - Military competition in space Out of view, but no less real a competition, the drive to develop space for military uses paralleled scientific efforts. Well before the launch of Sputnik 1, both the US and the USSR started developing plans for reconnaissance satellites. The Soviet Zenit spacecraft, which by the dual-use designed in by Korolev eventually became Vostok, began as a photoimaging satellite. It competed with the US Air Force's Discoverer series. Discoverer XIII provided the first payload recovered from space in August 1960 - ...
See also:Space Race, Space Race - Historical background, Space Race - Early military influences, Space Race - German contributions, Space Race - Cold War roots of the Space Race, Space Race - Artificial satellites start the race, Space Race - Sputnik, Space Race - Satellite communications, Space Race - Other noteworthy satellites, Space Race - More Soviet successes: Living creatures in space, Space Race - Animals in space, Space Race - Humans in space, Space Race - Lunar missions, Space Race - Unmanned probes, Space Race - Landing a human on the moon, Space Race - Other successes, Space Race - Missions to other planets, Space Race - Launches and docking, Space Race - Military competition in space, Space Race - The end of the Space Race, Space Race - Organization funding and the economic impact, Space Race - Deaths, Space Race - Timeline 1957-1975, Space Race - Legacy of the Space Race, Space Race - Advances in technology and education, Space Race - More space races to come?, Space Race - Notes Read more here: » Space Race: Encyclopedia II - Space Race - Military competition in space |
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| | | | | | Spaces: Encyclopedia II - Modulatory space - Cylindrical modulatory spaces A temperament of rank two which is not linear has one generator which is a fraction of an octave, called the period. We may represent the modulatory space of a such a temperament as n chains of generators in a circle, forming a cylinder. Here n is the number of periods in an octave.
For example, diaschismic temperament is the temperament which tempers out the diaschisma, or 2048/2025. It can be represented as two chains of slightly (3.25 to 3.55 cents) sharp fifths a half-octave apart, which can be depicted as two chains perpendicular ...
See also:Modulatory space, Modulatory space - Circles of generators, Modulatory space - Toroidal modulatory spaces, Modulatory space - Chains of generators, Modulatory space - Cylindrical modulatory spaces, Modulatory space - Five-limit modulatory space, Modulatory space - Seven-limit modulatory space Read more here: » Modulatory space: Encyclopedia II - Modulatory space - Cylindrical modulatory spaces |
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