A collection of subsets of a topological space X {\displaystyle X} is said to be locally finite if each point in the space has a neighbourhood that intersects...

term locally finite has a number of different meanings in mathematics: Locally finite collection of sets in a topological space Locally finite graph...

cover admits a point-finite open refinement. Every locally finite collection of subsets of a topological space is also point-finite. A topological space...

A collection in a space X {\displaystyle X} is countably locally finite (or 𝜎-locally finite) if it is the union of a countable family of locally finite...

Hausdorff and has a σ-locally finite base. A σ-locally finite base is a base which is a union of countably many locally finite collections of open sets. For...

σ-locally finite or countably locally finite collection is a family that is the union of countably many locally finite families. A cover F {\displaystyle...

countably locally discrete, if it is the countable union of locally discrete collections. 1. Locally discrete collections are always locally finite. See the...

locally finite (or σ-locally finite) if it is the union of a countable collection of locally finite collections of subsets of X. Cover A collection of...

topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by Dieudonné (1944). Every compact space...

{\displaystyle X_{1},X_{2},X_{3}\ldots } form a locally finite collection since a union of locally finite closed sets is closed. Similarly, it is true if...

there is no need to take finite intersections of such sets. The following theorem implies that if X {\displaystyle X} is a locally convex space then the...

contained in only finitely many sets in the cover. A cover is point finite if locally finite, though the converse is not necessarily true. Let C {\displaystyle...

Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical...

residually finite or finitely approximable if for every element g that is not the identity in G there is a homomorphism h from G to a finite group, such...

called locally finite if every point of X has a neighborhood U for which m(U) is finite. If m is locally finite, then it follows that m is finite on compact...

X to be pseudocompact requires that every locally finite collection of non-empty open sets of X be finite. There are many equivalent conditions for pseudocompactness...

homotopy class f ∈ [ X , K ] {\displaystyle f\in [X,K]} . For a locally finite collection of elements in H ∗ ( X ; A ) {\displaystyle H^{*}(X;A)} generating...

\{x\in \mathbb {Q} |x^{2}<2\}} . A complete lattice L is said to be locally finite if the supremum of any infinite subset is equal to the supremal element...

{\displaystyle G} is called locally finite if every finitely generated subgroup is finite. This is equivalent, in fact, to being 'ind-finite'. By applying Pontryagin...

that the collection of intervals must be finite is often dropped, especially in school mathematics, though it must still be locally finite, resulting...

generalizations of finite sets. In spaces that are compact in this sense, it is often possible to patch together information that holds locally—that is, in a...

The collection of Gâteaux holomorphic functions is denoted by HG(U,Y). In the analysis of Gateaux holomorphic functions, any properties of finite-dimensional...

the original space. It follows that, in the case where their number is finite, each component is also an open subset. However, if their number is infinite...

an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked by "arrows". A category has two basic properties:...

the finite intersection property (FIP) if the intersection over any finite subcollection of A {\displaystyle A} is non-empty. It has the strong finite intersection...

{R} ^{n}\rightarrow \mathbb {R} } is the maximum of a finite set of minimums of finite collections of polynomials. Rota's basis conjecture: for matroids...

measure μ {\displaystyle \mu } on a locally compact Hausdorff space that is inner regular, σ-finite, and locally finite but not outer regular is given by...

{\displaystyle a} is a limit point of S {\displaystyle S} , then any finite collection C {\displaystyle C} of open sets, such that each open set U ∈ C {\displaystyle...

locally compact Hausdorff spaces. In particular, any compactly supported continuous function on such a space is integrable with respect to any finite...

{\displaystyle X} are closed. The intersection of any collection of closed sets is also closed. The union of any finite number of closed sets is also closed. Using...