Let (X,𝒯) be a topological spaceMathworldPlanetmath. A subset 𝒜𝒯 is said to be a subbasis if the collectionMathworldPlanetmath of intersectionsDlmfMathworldPlanetmath of finitely many elements of 𝒜 is a basis ( for 𝒯.

Conversely, given an arbitrary collection 𝒜 of subsets of X, a topology can be formed by first taking the collection of finite intersections of members of 𝒜 and then taking the topology 𝒯 generated by as basis. 𝒯 will then be the smallest topology such that 𝒜𝒯.

Title subbasis
Canonical name Subbasis
Date of creation 2013-03-22 12:10:32
Last modified on 2013-03-22 12:10:32
Owner evin290 (5830)
Last modified by evin290 (5830)
Numerical id 10
Author evin290 (5830)
Entry type Definition
Classification msc 54A99
Synonym subbasic
Synonym subbasic
Synonym subbase
Related topic Basis
Related topic BasisTopologicalSpace