# Topological space

Revision as of 05:21, 1 December 2018 by Jflopezfernandez (talk | contribs)

A *topological space* is a pair $(X,\tau)$ consisting of a set $X$ and a collection $\tau$ of subsets of $X$, called open sets, satisfying the following axioms:^{[1]}

- $\emptyset, X \in \tau$
- If $\mathcal{O} \subset \tau$ then $\bigcup \mathcal{O} \in \tau$
- If $\{C_1,C_2, \ldots, C_n \}$ is a finite collection of closed sets, then $\bigcap_{n=1}^n C_n $ is a closed set.

It should be noted that the open sets in any metric space satisfy the conditions of a topological space. Therefore every metric space is also a topological space.^{[2]}