Definition 5.1.6 (First Countable).label Let $X$ be a topological space, then $X$ is first countable if for every $x \in X$, there exists a countable fundamental system of neighbourhoods at $x$.
Definition 5.1.6 (First Countable).label Let $X$ be a topological space, then $X$ is first countable if for every $x \in X$, there exists a countable fundamental system of neighbourhoods at $x$.
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