Locally compact space (9979 bytes)
1: ...on of the space looks like a small portion of a [[compact space]].
3: ...t [[iff]] every [[point]] has a [[local base]] of compact [[neighborhood (topology)|neighborhood]]s.
6: The various definitions of local compactness all coincide for [[Hausdorff space]]s.
7: ... article is thus primarily concerned with locally compact Hausdorff spaces.
11: === Compact Hausdorff spaces ===

Locally (975 bytes)
1: In [[mathematics]], something is said to occur ''locally'' if it occurs on "small enough" open sets. Give...
2: [[topological space]]s, two spaces are locally equivalent if every point of the first space has ...
4: ...son, one may say that the circle and the line are locally equivalent.
6: Similarly, the sphere are the plane are locally equivalent. A small enough observer standing on...

Locally ringed space (6221 bytes)
1: ...ought of as "functions" defined on that open set. Locally ringed spaces appear throughout [[mathematical an...
5: A locally ringed space is a [[topological space]] ''X'', to...
7: ...' is also called the '''structure sheaf''' of the locally ringed space ''X'', and is denoted by ''O''<sub>'...
13: ...-analytic]] functions. Both of these give rise to locally ringed spaces.
15: ...nged spaces. [[Scheme (mathematics)|Schemes]] are locally ringed spaces obtained by "gluing together" spect...

Locally constant function (2657 bytes)
3: ...cal space]] ''A'' to a [[set]] ''B'' is called '''locally constant''', [[iff]] for every ''a'' in ''A'' the...
5: Every constant function is locally constant.
7: ...&pi;]], and ''f''(''x'') = 1 for ''x'' > &pi;, is locally constant (here we use the fact that &pi; is [[irr...
9: ... component]] of ''A''. The converse is true for [[locally connected]] spaces (where the connected component...
12: ...up>-1</sup>(''x'') over ''x''; this assignment is locally constant.

Locally cyclic group (1666 bytes)
1: In [[mathematics]], a '''locally cyclic group''' is a group (''G'', *) in which ev...
4: *Every cyclic group is locally cyclic, and every locally cyclic group is [[abelian group|abelian]].
5: *Every finitely-generated locally cyclic group is cyclic.
6: ...d [[quotient group]] of a locally cyclic group is locally cyclic.
7: *A group is locally cyclic if and only if every pair of elements in t...

Locally modified software (360 bytes)

Semi-locally simply connected (1459 bytes)
2: ..., a [[topological space]] ''X'' is called '''semi-locally simply connected''' if every [[point]] ''x'' in '...
4: ...connected. An example of a space that is not semi-locally simply connected is the [[Hawaiian earring]]: the...
6: ...locally simply connected, but it is clearly not [[locally simply connected]].
8: ...connected]], [[locally path-connected]], and semi-locally simply connected.

Locally convex topological vector space (1481 bytes)
2: '''locally convex''' if its [[topology]] is defined by a set...
3: ...)|neighborhood]]s of 0. Every [[normed space]] is locally convex, since the [[triangle inequality]] ensures...
5: ...locally convex topological vector space''' (or '''locally convex space''') is a [[topological vector space]...
7: ...a locally convex space, and much of the theory of locally convex spaces generalises parts of the theory of...
9: ...p''</sup> spaces]] for <math>0<p<1</math> are not locally convex.

List of locales in Britain where ant species have become locally extinct (1831 bytes)

Compact (723 bytes)
1: ...cialized usages of the terms '''compact''' and '''compactness''' exist.
3: * Multiple definitions of the term "compact" are found in [[mathematics]]:
4: ...lso includes the closely related notion of a '''[[compact set]]'''.
5: ... (though not entirely unrelated) notion of a '''[[compact element]]''' is typically used.
6: * A '''[[Compact Flash]]''' is a type of [[data storage device]].

Relatively compact subspace (1362 bytes)
1: ...[topological closure|closure]] is [[compact space|compact]].
3: ... in ''X''. This condition is also called '''''pre-compact''''' or '''''relatively bounded'''''.
5: ...terises relatively compact subsets in certain non-compact [[homogeneous space]]s (specifically spaces of [[...
7: ...o with the translates of ''F'' being a relatively compact set. This needs to be made precise in terms of th...

Compact government (479 bytes)
1: '''Compact governments''' or '''compacts''' were the conservative colonial cliques
2: ...al elite. The best known compact was the [[Family Compact]] that ruled [[Upper Canada]]. There was a simila...

Compact operator (2453 bytes)
3: ...it of finite rank operators, so that the class of compact operators can be defined alternatively as the clo...
5: ...ompact operator ''K'' on [[function space]]s; the compactness property is shown by [[equicontinuity]]. The ...
7: ...yes Riesz]] (published [[1918]]). It shows that a compact operator ''K'' on an infinite-dimensional Banach ...
9: ... operators between two Banach spaces. Indeed, the compact operators on a Hilbert space form a [[maximal ide...
11: Examples of compact operators include [[Hilbert-Schmidt operator]]s, ...

Dark compact (547 bytes)
1: ...e [[horror fiction]] and [[fantasy]] genres. Dark compacts are colloquially known as "deals with the devil"...

Compact element (3632 bytes)
1: ...t element. Note that there are other notions of [[compactness]] in mathematics and that the term [[finite]]...
3: ...s. Posets that can be recovered from their set of compact elements are called [[algebraic poset]]s.
7: ...''P'',&le;) an element ''c'' of ''P'' is called ''compact'' (or ''finite'') if it satisfies one of the foll...
19: ...ays compact. It may well be that this is the only compact element, as the example of the [[real number|real...
23: ...et inclusion]]. Within this complete lattice, the compact elements are exactly the finite sets. This justif...

Compact group (3397 bytes)
1: ... unless ''G'' happens to be finite. But it is the compact Hausdorff groups, natural generalisations of [[fi...
3: ...as well as mathematics. Also every [[torus]] is a compact group.
5: ...pact group. This means that [[Galois group]]s are compact groups, a basic fact for the theory of [[algebrai...
7: Compact groups all carry a [[Haar measure]], which will b...
9: ... to give the detailed [[character theory]] of the compact connected Lie groups, based on [[maximal torus]] ...

Compact (newspaper) (751 bytes)
1: A '''compact newspaper''' is a [[United Kingdom|British]] term...

UN Global Compact (3546 bytes)
1: ...he challenged business leaders to join the Global Compact to bring companies together with UN agencies, lab...
3: The Global Compact was officially launched at UN Headquarters in New...
5: ...an extensive consultation process with all Global Compact participants.
7: The '''Global Compact Office''' is supported by six UN agencies: the [[...
34: The Global Compact is not a regulatory instrument, but rather a foru...

Interstate compact (1246 bytes)
1: ...transportation]] infrastructure. In some cases, a compact serves simply as a coordination mechanism between...
11: == Non-operating interstate compacts ==
12: *[[Northeast Dairy Compact]] (formerly set fluid [[milk]] prices the [[New E...

Family Compact (2439 bytes)
1: ...]. It was one of a number of [[Tory]]-dominated [[Compact government]]s that ruled the colonies of [[Britis...
3: ...au Clique|Château Clique]]. Members of the Family Compact were described as adherents of "rabid Toryism" by...
5: ...bly with little real power. Members of the Family Compact ensured their conservative friends held the impor...
7: The Family Compact was centred in [[Toronto, Ontario|Toronto]], then...
9: ... [[Francis Bond Head]] (a supporter of the Family Compact) as Lieutenant Governor in [[1838]].

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