Initial topology
In general topology and related areas of mathematics, the initial topology (or induced topology or weak topology or limit topology or projective topology) on a set , with respect to a family of functions on , is the coarsest topology on X that makes those functions continuous. The subspace topology and product topology constructions are both special cases of initial topologies. Indeed, the initial topology construction can be viewed as a generalization of these.
Cap productCategory of topological spacesCoarse topologyCompact-open topologyComparison of topologiesContinuous functionContinuous functions on a compact Hausdorff spaceEvaluation mapFinal topologyFinite measureGeneral topologyInduced topologyInductive tensor productInverse limitLF-spaceList of topologiesLocally convex topological vector spaceNatural topologyProduct topologyProjective limit topologyProjective topologySierpiński spaceStrong operator topologySubbaseTopological indistinguishabilityTychonoff spaceUniformizable spaceWeak topologyWeakest topology
Link from a Wikipage to another Wikipage
primaryTopic
Initial topology
In general topology and related areas of mathematics, the initial topology (or induced topology or weak topology or limit topology or projective topology) on a set , with respect to a family of functions on , is the coarsest topology on X that makes those functions continuous. The subspace topology and product topology constructions are both special cases of initial topologies. Indeed, the initial topology construction can be viewed as a generalization of these.
has abstract
In general topology and relate ...... es those functions continuous.
@en
Link from a Wikipage to an external page
Wikipage page ID
page length (characters) of wiki page
Wikipage revision ID
968,750,666
Link from a Wikipage to another Wikipage
title
Initial topology
@en
Product topology and subspace topology
@en
wikiPageUsesTemplate
subject
comment
In general topology and relate ...... as a generalization of these.
@en
label
Initial topology
@en