- sequential compactness
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Mahler's compactness theorem — In mathematics, Mahler s compactness theorem, proved by Kurt Mahler (1946), is a foundational result on lattices in Euclidean space, characterising sets of lattices that are bounded in a certain definite sense. Looked at another way, it… … Wikipedia
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… … Wikipedia
Tychonoff's theorem — For other theorems named after Tychonoff, see Tychonoff s theorem (disambiguation). In mathematics, Tychonoff s theorem states that the product of any collection of compact topological spaces is compact. The theorem is named after Andrey… … Wikipedia
Limit point compact — In mathematics, particularly topology, limit point compactness is a certain condition on a topological space which generalizes some features of compactness. In a metric space, limit point compactness, compactness, and sequential compactness are… … Wikipedia
Metric space — In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3 dimensional Euclidean… … Wikipedia
Countably compact space — In mathematics a topological space is countably compact if every countable open cover has a finite subcover. Examples and Properties A compact space is countably compact. Indeed, directly from the definitions, a space is compact if and only if it … Wikipedia
Eberlein–Šmulian theorem — In the mathematical field of functional analysis, the Eberlein–Šmulian theorem is a result relating three different kinds of weak compactness in a Banach space. The three kinds of compactness for a subset A of a topological space are: *… … Wikipedia
Pseudocompact space — In mathematics, in the field of topology, a topological space is said to be pseudocompact if its image under any continuous function to R is bounded.Conditions for pseudocompactness*Every countably compact space is pseudocompact. For normal… … Wikipedia
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,… … Wikipedia
Generalised metric — In mathematics, the concept of a generalised metric is a generalisation of that of a metric, in which the distance is not a real number but taken from an arbitrary ordered field.In general, when we define metric space the distance function is… … Wikipedia
