I am reading a topology definition:
Let $X$ be a set and let $\tau$ be a family of subsets of $X$. Then $\tau$ is called a topology on $X$ if:
- Both the empty set and $X$ are elements of $\tau$
- Any union of elements of $\tau$ is an element of $\tau$
- Any intersection of finitely many elements of $\tau$ is an element of $\tau$
If $\tau$ is a topology on $X$, then the pair $(X, \tau)$ is called a topological space. The notation $X_\tau$ may be used to denote a set $X$ endowed with the particular topology $\tau$. The members of $\tau$ are called open sets in $X$.
My question is Are the members of $\tau$, open sets or only is called opens set?