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...

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...

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

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...

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...

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

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

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...

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...

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

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

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...

every compact subset of its domain of definition. The importance of such functions lies in the fact that their function space is similar to Lp spaces, but...

{T}})} is a locally compact space, then f n → f {\displaystyle f_{n}\to f} compactly if and only if f n → f {\displaystyle f_{n}\to f} locally uniformly...

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...

countably compact space is countably compact. Every countably compact space is pseudocompact. In a countably compact space, every locally finite family...

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

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

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...

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...

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...

sequence is locally uniformly convergent. Every locally uniformly convergent sequence is compactly convergent. For locally compact spaces local uniform...

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

In algebra, a locally compact field is a topological field whose topology forms a locally compact Hausdorff space. These kinds of fields were originally...

"locally compact and sigma-compact spaces are paracompact in nLab". ncatlab.org. Leon Ehrenpreis, Theory of Distributions for Locally Compact Spaces,...

necessarily locally convex. Banach spaces, Hilbert spaces and Sobolev spaces are other well-known examples of TVSs. Many topological vector spaces are spaces 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...

differentiable structure that the topological space supports.) The real line is a locally compact space and a paracompact space, as well as second-countable and normal...

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