Base

(Topology)

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Topology
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What is Base (topology)?

In mathematics, a base (or basis) B of a topology on a set X is a collection of subsets of X such that every finite intersection of elements of B (including X itself, which is, by a standard convention, the empty intersection) is a union of elements of B. A base defines (one says also generates) a topology on X that has, as open sets, all unions of elements of B. Bases have been introduced because some topologies have a base consisting of open sets that have specific useful properties. This is typically the case for the Zariski topology on the spectrum of a ring. For the usual basis of this topology, every finite intersection of basis elements is a basis element. Therefore bases are sometimes required to be stable by finite intersection.

Technology Types

archivebibliographic databases and indexecomputational group theorydepositoryfacilityfamilygeneral topologygroup theoryinternet search engineopen access (publishingopen access archivepermutation groupscholarly search servicesearch engineset familysocial grouptopologyweb sitewebsite

Synonyms

BaseBASEBase-search.netBasisBielefeld Academic Search EngineCountable baseOpen basisTopological baseTopological basis

Translations

Bas (topologi) (sv)Basis (Topologie) (de)Basis (topologie) (nl)Baza przestrzeni topologicznej (pl)Báze topologického prostoru (cs)Bazo (grupa teorio) (eo)База топологии (ru)База топології (uk)기저 (위상수학) (ko)基 (拓撲學) (zh)基底 (位相空間論) (ja)

Tech Info


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