Topological space

This article is about a basic definition in topology.
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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 $\mathfrak{T}$