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precompact space

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  • Precompact set — In topology and related branches of mathematics, a precompact set, or pre compact set, may be either: * A relatively compact set; or * A totally bounded set.(These are equivalent in a complete metric space.) …   Wikipedia

  • Totally bounded space — In topology and related branches of mathematics, a totally bounded space is a space that can be covered by finitely many subsets of any fixed size (where the meaning of size depends on the given context). The smaller the size fixed, the more… …   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

  • Uniform property — In the mathematical field of topology a uniform property or uniform invariant is a property of a uniform space which is invariant under uniform isomorphisms.Since uniform spaces come are topological spaces and uniform isomorphisms are… …   Wikipedia

  • Tightness of measures — In mathematics, tightness is a concept in measure theory. The intuitive idea is that a given collection of measures does not escape to infinity. Contents 1 Definitions 2 Examples 2.1 Compact spaces 2.2 …   Wikipedia

  • Normal family — In mathematics, with special application to complex analysis, a normal family is a pre compact family of continuous functions. Informally, this means that the functions in the family are not exceedingly numerous or widely spread out; rather, they …   Wikipedia

  • Spectral theory of compact operators — In functional analysis, compact operators are linear operators that map bounded sets to precompact ones. Compact operators acting on a Hilbert space H is the closure of finite rank operators in the uniform operator topology. In general, operators …   Wikipedia

  • Palais-Smale compactness condition — The Palais Smale compactness condition is a necessary condition for some theorems of the calculus of variations.The condition is necessary because the calculus of variations studies function spaces that are infinite dimensional some extra notion… …   Wikipedia

  • Topologie discrète — Pour les articles homonymes, voir Discret. En mathématiques, plus précisément en topologie, la topologie discrète sur un ensemble est une structure d espace topologique où, de façon intuitive, tous les points sont « isolés » les uns des …   Wikipédia en Français

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