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Second Countable Space

Last updated Nov 1, 2022

# Definition

Let $X$ be a Topological Space. We say $X$ is Second Countable if there exists a Countable Topological Basis for $X$.

# Examples

  1. One major example is Euclidean Space is Second Countable.
  2. A simple nonexample is $\mathbb{R}$ equipped with the Discrete Topology