Open set

A member of a given topology

Tricks

• It is quite convenient to decompose an open set to the elements of topology-base: $$ U = \bigcup_{\alpha \in A} U_{\alpha} = \bigcup_{\alpha \in A} \bigcap_{k = 1}^{K_{\alpha}} V_{\alpha, k} $$ and then consider pre-base or base elements instead of an abstract open set.