Topological space

This article is about a basic definition in topology.
VIEW: Definitions built on this | Facts about this | Survey articles about this
View a complete list of basic definitions in topology

Definition

A topological space is a set endowed with a topology. A topology on a set $S$ is a collection ${\mathfrak {T}}$ of subsets of the set, called open subsets, satisfying the following:

• The empty set and the whole space are in ${\mathfrak {T}}$
• An arbitrary union of members of ${\mathfrak {T}}$ is in ${\mathfrak {T}}$
• A finite intersection of members of ${\mathfrak {T}}$ is in ${\mathfrak {T}}$