Question

What does topological space mean?

Answer 1

Topological space definition:

A topological space is a pair $(X,T)$ where $X$ is a set and $T$ is a collection of subsets of $X$ with the following properties:

• The empty set and $X$ are both in $T$,
• Any (finite or infinite) union of sets in $T$ is itself in $T$, and
• Any finite intersection of sets in $T$ is itself in $T$,

Hence the ordered pair $(X,T)$ is called a topological space.