Topological space (19036 bytes)
1: ...he branch of mathematics that studies topological spaces in their own right is called [[topology]].
5: A '''topological space''' is a [[set]] ''X'' together with a collection ...
15: ...be placed on nearly any set to form a topological space. When every set in a topology ''T''₁ i...
19: ...m. From the standpoint of topology, homeomorphic spaces are essentially identical.
21: ...topological spaces]], '''Top''', with topological spaces as [[object (category theory)|objects]] and cont...

Topological vector space (7707 bytes)
1: ...ector space]] which is endowed with a [[Hausdorff space|Hausdorff]] [[topology]] such that vector additio...
3: ...al analysis]]. The elements of topological vector spaces are typically [[function (mathematics)|function]...
7: ...bert space]]s) are examples of topological vector spaces.
9: ...t ''f''(''x'') for every real number ''x''. This space is complete, but not normable.
11: Spaces of differentiable functions give other non-norma...

Locally convex topological vector space (1481 bytes)
1: ...n [[functional analysis]], a [[topological vector space]] is called
3: ...d (topology)|neighborhood]]s of 0. Every [[normed space]] is locally convex, since the [[triangle inequal...
5: ...s. Although such a space need not be [[Hausdorff_space|Hausdorff]], this is often also assumed.
7: ...spaces generalises parts of the theory of Banach spaces. Indeed, local convexity is a generalisation of...
9: ... On the other hand, [[Lp space|L^''p'' spaces]] for <math>0<p<1</math> are not locally convex.

Topological defect (2584 bytes)
1: ...own in regions that spread at the speed of light; topological defects occur where different regions came into c...
3: Various different types of topological defects are possible with the type of defect form...
10: ...n artificial Earth-bound physics experiments, but topological defects that formed during the universe's formati...
12: No topological defects of any type have yet been observed by ast...
14: See also [[topological soliton]]

Topological property (584 bytes)
1: ...cal invariant''' is a property of a [[topological space]] which is [[invariant_(mathematics)|invariant]] ...
3: ==Topological properties==
8: *[[compact space|compactness]]
10: *[[Hausdorff space|Hausdorff]]

Topological sorting (2032 bytes)
1: ...re all nodes to which it has edges. Any DAG has a topological sort, and in fact most have many.
5: ...e completed before job ''y'' can be done. Then, a topological sort gives an order in which to perform the jobs....
9: | The graph shown to the left has many valid topological sorts, including:
18: The usual algorithm for topological sorting has running time linear in the number of ...
32: ...NIST Dictionary of Algorithms and Data Structure: topological sort]

Soliton (topological) (1115 bytes)
1: A '''topological [[soliton]]''' is a solution of a system of [[par...
3: ...cording to Kibble-Higgs mechanism. The well known topological defects are [[magnetic monopoles]], [[cosmic stri...

Topological group (6068 bytes)
1: ...require that the topology on ''G'' be [[Hausdorff space|Hausdorff]]. The reasons, and some equivalent con...
3: ...tigated in [[mathematical analysis|analysis]] are topological groups (usually with some additional structure).
7: ...[[discrete group]]s. In this sense, the theory of topological groups subsumes that of ordinary groups.
9: ...h as [[Banach space]]s or [[Hilbert space]]s, are topological groups.
11: ... as a [[subspace (topology)|subset]] of Euclidean space '''R'''^{''n''&times;''n''}.

Topological ring (2833 bytes)
1: ...gebra)|ring]] ''R'' which is also a [[topological space]] such that both the addition and the multiplicat...
9: ...x number]]s and [[dual numbers]] form alternative topological rings. See [[hypercomplex numbers]] for higher di...
11: ...cal ring. The ''I''-adic topology is [[Hausdorff space|Hausdorff]] if and only if the [[intersection (se...
17: ...logy on ''R'' equals the [[subspace (topology)|subspace topology]] arising from ''S''.
20: ... most naturally defined as completions of certain topological rings carrying ''I''-adic topologies.

Topological Boolean algebra (548 bytes)
1: ...abstract algebra]] and [[mathematical logic]], '''topological Boolean algebra''' is one of the many names that ...
3: ... [[Lattice (order)|complement]] are [[topological space|continuous functions]].

Category of topological spaces (2477 bytes)
1: ...y of '''Top''' and of properties of [[topological space]]s using the techniques of [[category theory]] is...
3: ...e name '''Top''' for the category with [[Manifold|topological manifolds]] as objects and continuous maps as mor...
7: ...[[singleton (mathematics)|singleton]] topological space is a [[terminal object]]. There are thus no [[zer...
9: ...is given by the [[disjoint union]] of topological spaces. By using the [[quotient topology]], one can the...
13: ...t]] (which equips a given set with the [[discrete space|discrete topology]]) and a right adjoint (which e...

Topological abelian group (674 bytes)
1: ...opological abelian group''', or '''TAG''', is a [[topological group]] that is also an [[abelian group]].
2: ...h a [[group (algebra)|group]] and a [[topological space]], the group operations are [[continuous (topolog...
4: The theory of topological groups applies also to TAGs, but more can be done...
9: [[Category:Topological groups]]

Topological quantum field theory (409 bytes)
1: '''Topological quantum field theory''' in [[theoretical physics]...

Lp space (7041 bytes)
1: {{wrongtitle|title=L^p space}}.
3: ... space]]s. See also [[root mean square]], [[Hardy space]].
5: ==''L^p'' spaces==
7: ...l number]] and let ''S'' be a Euclidean [[measure space]] equipped with [[Lebesgue measure]]. Consider th...
13: The space L^&infin;(''S''), while related, is def...

New Space (310 bytes)
1: The '''New Space''' (''Nuevo Espacio'') is a [[social democrat]]ic...

T1 space (7558 bytes)
1: {{wrongtitle|title=T₁ space}}
2: ...s''' are particularly nice kinds of [[topological space]]s.
7: Let ''X'' be a [[topological space]] and let ''x'' and ''y'' be points in ''X''. We ...
9: *''X'' is a '''T₁ space''' if any two [[distinct]] points in ''X'' can be...
11: ...''X'' is a '''R₀ space''' if any two [[topologically distinguishable]] points in ''X'' can be separa...

F-space (994 bytes)
1: ...tional analysis]], an '''F-space''' is a [[vector space]] ''V'' over the [[real number|real]] or [[comple...
5: # The metric space (''V'', ''d'') is [[completeness (topology)|compl...
7: ...chet space]] is reserved for [[locally convex]] F-spaces.
9: ...nach space]]s and [[Fr&eacute;chet space]]s are F-spaces.
10: ...examples of F-spaces which are not Fr&eacute;chet spaces.

Space: Above and Beyond (2317 bytes)
1: '''''Space: Above and Beyond''''' was a short-lived [[United...
3: ...arines]], flying [[Hammerhead]] missions from the spacecraft carrier USS Saratoga in the year 2063.

Space-like (643 bytes)
1: ...arated points (or events) in [[spacetime]] have a spacetime interval less than 0 (see [[sign convention]]...
3: ...se dimensions correspond to spatial dimensions of spacetime (e.g. x,y,z).

Space (4969 bytes)
1: The word '''space''' has many meanings, including:
4: ...ntentious. Various concepts used to try to define space have included:
10: ...ysics]] examines [[spacetime]] rather than space; spacetime is modeled as a four-dimensional [[manifold]]...
16: ...s is to ask, "Can space itself be measured, or is space part of the measurement system?" The same debate...
18: ... comprehend sense experience. With Kant, neither space nor time are conceived as [[substance]]s, but rat...

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