# locally compact

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**locally compact**— adjective (of a topological space) That for every point of the given topological space, there is a neighborhood of that point whose closure is compact …2

**Locally compact space**— In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.Formal definitionLet X be a topological space. The… …3

**Locally compact group**— In mathematics, a locally compact group is a topological group G which is locally compact as a topological space. Locally compact groups are important because they have a natural measure called the Haar measure. This allows one to define… …4

**Locally compact quantum group**— The locally compact (l.c.) quantum group is a relatively new C* algebraic formalism for quantum groups, generalizing the Kac algebra, compact quantum group and Hopf algebra approaches. Earlier attempts of a unifying definition of quantum groups… …5

**locally compact space**— Math. a topological space in which each point has a neighborhood that is compact. * * * …6

**locally compact space**— Math. a topological space in which each point has a neighborhood that is compact …7

**Locally convex topological vector space**— In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… …8

**Compact space**— Compactness redirects here. For the concept in first order logic, see compactness theorem. In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness… …9

**Locally connected space**— In this topological space, V is a neighbourhood of p and it contains a connected neighbourhood (the dark green disk) that contains p. In topology and other branches of mathematics, a topological space X is locally connected if every point admits… …10

**Locally regular space**— In mathematics, particularly topology, a topological space X is locally regular if intuitively it looks locally like a regular space. More precisely, a locally regular space satisfies the property that each point of the space belongs to a subset… …11

**Locally normal space**— In mathematics, particularly topology, a topological space X is locally normal if intuitively it looks locally like a normal space. More precisely, a locally normal space satisfies the property that each point of the space belongs to a… …12

**Compact-open topology**— In mathematics, the compact open topology is a topology defined on the set of continuous maps between two topological spaces. The compact open topology is one of the commonly used topologies on function spaces, and is applied in homotopy theory… …13

**Compact convergence**— In mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence which generalizes the idea of uniform convergence. It is associated with the compact open topology. Contents 1 Definition 2 Examples 3 Properties …14

**Compact operator on Hilbert space**— In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… …15

**Compact group**— In mathematics, a compact (topological, often understood) group is a topological group whose topology is compact. Compact groups are a natural generalisation of finite groups with the discrete topology and have properties that carry over in… …16

**Locally finite collection**— In the mathematical field of topology, local finiteness is a property of collections of subsets of a topological space. It is fundamental in the study of paracompactness and topological dimension. A collection of subsets of a topological space X… …17

**Locally integrable function**— In mathematics, a locally integrable function is a function which is integrable on any compact set of its domain of definition. Formal definition Formally, let Omega be an open set in the Euclidean space scriptstylemathbb{R}^n and scriptstyle… …18

**Σ-compact space**— In mathematics, a topological space is said to be sigma; compact if it is the union of countably many compact subspaces. A space is said to be sigma; locally compact if it is both sigma; compact and locally compact.Properties and Examples* Every… …19

**Continuous functions on a compact Hausdorff space**— In mathematical analysis, and especially functional analysis, a fundamental role is played by the space of continuous functions on a compact Hausdorff space with values in the real or complex numbers. This space, denoted by C(X), is a vector… …20

**Maximal compact subgroup**— In mathematics, a maximal compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst such subgroups. Maximal compact subgroups play an important role in the classification of …