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#first-countable_space

First-countable space

Topological space where each point has a countable neighbourhood basis

In topology, a branch of mathematics, a first-countable space is a topological space satisfying the "first axiom of countability". Specifically, a space is said to be first-countable if each point has a countable neighbourhood basis. That is, for each point in there exists a sequence of neighbourhoods of such that for any neighbourhood of there exists an integer with contained in Since every neighborhood of any point contains an open neighborhood of that point, the neighbourhood basis can be chosen without loss of generality to consist of open neighborhoods.

Fri 15th

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First-countable space Second-countable space Countably compact space Separable space Axiom of countability Sequential space Probability space Sequentially compact space Countable set Paracompact space

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