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Let $X$ be a topological space with topology $\mathscr{T}$. An open set $U$ is in $\mathscr{T}$. Therefore, a topological space may be defined as a set $X$ together with a collection of subsets of $X$, called open sets, such that $\emptyset$ and $X$ are both open, and such that arbitrary unions and finite intersections of open sets are open.[1]


  1. Munkres, James R. Topology, 2015. pg. 74.