Source: wikibot/first-countable-space
= First-countable space
{wiki=First-countable_space}
In topology, a topological space \\( X \\) is called *first-countable* if, at every point \\( x \\in X \\), there exists a countable collection of open sets (called a *countable neighborhood basis*) such that any open neighborhood of \\( x \\) contains at least one of these open sets.