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- W1024833145 abstract "For a set S, a family of subsets of S is called a cover if the union ⋃{A: A ∈ } is S. A cover C of S is called finite if the cardinality of C is finite. For two covers B and C of S, B is a refinement of C (or B refines C) if each member of B is contained in some member of C. In particular, B is called a subcover of C if B is a subfamily of C. A cover C of S has a finite refinement if it has a finite subcover. In a topological space X, a cover of X is called an open cover (a closed cover) if each member of is open (closed) in X. A family of subsets of X is a locally finite family if each point of X has an open neighborhood that meets at most finitely many members of . A space X is called paracompact if every open cover of X has a locally finite open refinement. Paracompactness seems to be the most important covering property of spaces. This chapter describes various covering properties in terms of several variations of local finiteness." @default.
- W1024833145 created "2016-06-24" @default.
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- W1024833145 date "2003-01-01" @default.
- W1024833145 modified "2023-09-27" @default.
- W1024833145 title "Covering Properties" @default.
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- W1024833145 doi "https://doi.org/10.1016/b978-044450355-8/50017-9" @default.
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