first countable

Let $X$ be a topological space and let $x\in X$. $X$ is said to be at $x$ if there is a sequence ${(B_n)}_{n\in \mathbb{N}}$ of open sets such that whenever $U$ is an open set containing $x$, there is $n\in \mathbb{N}$ such that $x\in B_n\subseteq U$.

The space $X$ is said to be if for every $x\in X$, $X$ is first countable at $x$.

Remark. Equivalently, one can take each $B_n$ in the sequence to be open neighborhood of $x$.