Second-Countable Space

Definition

A second-countable space is a Topological Space whose Topology has a countable basis.

Facts

Every second-countable space is a Separable Space.

$n$-dimension Euclidean Space ${\mathbb{R}}^2$ where $n\in \mathbb{N}$, is a second-countable space.

Hilbert Space $H$ is a second-countable space.

The Product Space of two second-countable spaces is a second-countable space.

Every Second-Countable Space is a Lindelof space.

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