Topological Spaces

A topological space is a set $X$ equiped with a collection of subsets $T\subseteq \mathcal{P}X$ called open sets, such that:

• $\varnothing \in T$ and $X\in T$
• $\bigcap S\in T$ for $S\subseteq T$, $|S|$ countable.
• $\bigcup S\in T$ for $S\subseteq T$ ($|S|$ arbitrary).

Source

https://mathworld.wolfram.com/TopologicalSpace.html