# compactness

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**Lindelöf space**— In mathematics, a Lindelöf space is a topological space in which every open cover has a countable subcover. A Lindelöf space is a weakening of the more commonly used notion of compactness , which requires the existence of a finite subcover.A… …62

**Cover (topology)**— In mathematics, a cover of a set X is a collection of sets whose union contains X as a subset. Formally, if is an indexed family of sets Uα, then C is a cover of X if Contents 1 Cover in t …63

**List of general topology topics**— This is a list of general topology topics, by Wikipedia page. Contents 1 Basic concepts 2 Limits 3 Topological properties 3.1 Compactness and countability …64

**List of theorems**— This is a list of theorems, by Wikipedia page. See also *list of fundamental theorems *list of lemmas *list of conjectures *list of inequalities *list of mathematical proofs *list of misnamed theorems *Existence theorem *Classification of finite… …65

**Relatively compact subspace**— In mathematics, a relatively compact subspace (or relatively compact subset) Y of a topological space X is a subset whose closure is compact.Since closed subsets of compact spaces are compact, every set in a compact space is relatively compact.… …66

**Infinitary logic**— Those unfamiliar with mathematical logic or the concept of ordinals are advised to consult those articles first. An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Some infinitary logics may have… …67

**Gromov's theorem**— may mean one of a number of results of Mikhail Gromov:*One of Gromov s compactness theorems: ** Gromov s compactness theorem (geometry) in Riemannian geometry ** Gromov s compactness theorem (topology) in symplectic topology *Gromov s Betti… …68

**Second-countable space**— In topology, a second countable space, also called a completely separable space, is a topological space satisfying the second axiom of countability. A space is said to be second countable if its topology has a countable base. More explicitly,… …69

**Elementary class**— In the branch of mathematical logic called model theory, an elementary class (or axiomatizable class) is a class consisting of all structures satisfying a fixed first order theory. Contents 1 Definition 2 Conflicting and alternative terminology …70

**List of mathematics articles (G)**— NOTOC G G₂ G delta space G networks Gδ set G structure G test G127 G2 manifold G2 structure Gabor atom Gabor filter Gabor transform Gabor Wigner transform Gabow s algorithm Gabriel graph Gabriel s Horn Gain graph Gain group Galerkin method… …