Let $X$ be a topological space and let $x\in X$ $X$ is said to be <</SPAN>#46#>first countable 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 first countable if for every $x\in X$ $X$ is first countable at $x$