topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space. More precisely...

space is said to be σ-compact if it is the union of countably many compact subspaces. A space is said to be σ-locally compact if it is both σ-compact...

mathematics, a locally compact group is a topological group G for which the underlying topology is locally compact and Hausdorff. Locally compact groups are...

a topological space X {\displaystyle X} is called a compactly generated space or k-space if its topology is determined by compact spaces in a manner made...

compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has...

of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize...

K} is complete. Compact space Locally compact space Measure of non-compactness Orthocompact space Paracompact space Relatively compact subspace Sutherland...

topological space is locally finite iff its a locally finite cover of the underlying locale. Every compact space is paracompact. Every regular Lindelöf space is...

physics, a locally compact quantum group is a relatively new C*-algebraic approach toward quantum groups that generalizes the Kac algebra, compact-quantum-group...

while any compact Hausdorff space is locally compact, a connected space—and even a connected subset of the Euclidean plane—need not be locally connected...

restrict to locally compact Hausdorff spaces, and only consider the measures that correspond to positive linear functionals on the space of continuous...

Like all manifolds, it is locally homeomorphic to Euclidean space and thus locally metrizable (but not metrizable) and locally Hausdorff (but not Hausdorff)...

representation theorem relates linear functionals on spaces of continuous functions on a locally compact space to measures in measure theory. The theorem is...

finite-dimensional vector space over the reals or a p-adic field. The Pontryagin dual of a locally compact abelian group is the locally compact abelian topological...

a homology theory for locally compact spaces, introduced by Armand Borel and John Moore in 1960. For reasonable compact spaces, Borel−Moore homology coincides...

metric. Every compact Riemann surface of genus greater than 1 (with its usual metric of constant curvature −1) is a locally symmetric space but not a symmetric...

convergent sequence of continuous functions fn on either metric space or locally compact space is continuous. If, in addition, fn are holomorphic, then the...

space is σ-compact (i.e., a countable union of compact subsets.) If there is an exhaustion by compact sets, the space is necessarily locally compact (if...

locally compact groups is however much weaker than the Tannaka–Krein duality theory for compact topological groups or Pontryagin duality for locally compact...

is compact. As a result, every (weakly) locally compact space is core-compact, and every Hausdorff (or more generally, sober) core-compact space is locally...

Euclidean space. In particular, they are locally compact, locally connected, first countable, locally contractible, and locally metrizable. Being locally compact...

to functions defined on normed vector spaces and the other applying to functions defined on locally compact spaces. Aside from this difference, both of...

locally compact. If a hemicompact space is weakly locally compact, then it is exhaustible by compact sets. If X {\displaystyle X} is a hemicompact space, then...

to locally finite open covers. The Hausdorff versions of these statements are: every locally compact Hausdorff space is Tychonoff, and every compact Hausdorff...

paracompact space; and has some Z {\displaystyle Z} in Φ {\displaystyle \Phi } which is a neighbourhood. If X {\displaystyle X} is a locally compact space, assumed...

topology) are locally compact abelian groups. A topological group is called locally compact if the underlying topological space is locally compact and Hausdorff;...

B;E)} is an isomorphism. Let X be a locally compact topological space. (In this article, a locally compact space is understood to be Hausdorff.) For a...

Normed space – Vector space on which a distance is definedPages displaying short descriptions of redirect targets Locally compact field Locally compact group –...

of non-compactness Paracompact space Locally compact space Compactly generated space Axiom of countability Sequential space First-countable space Second-countable...

Hausdorff spaces aren't generally regular, a Hausdorff space that is also (say) locally compact will be regular, because any Hausdorff space is preregular...