Open Set (Topology)

In topology

In topology, open sets are basic concepts defined axiomatically as subsets that satisfy certain conditions.

In Metric Space

A set $X\subseteq Y$ is open iff For every point $x\in X$, there is some radius $ϵ\in \mathbb{R}$ such that the open ball of radius $ϵ$ at $x$, $B_{ϵ}(x)\subset X$.