Definition:Second-Countable Space
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Definition
A topological space $T = \struct {S, \tau}$ is second-countable or satisfies the Second Axiom of Countability if and only if its topology has a countable basis.
Also known as
Also known as:
Some sources render this without the hyphen: second countable.
$\mathsf{Pr} \infty \mathsf{fWiki}$ aims to be consistent in presentation, and the hyphenated version is preferred.
Also see
- Results about second-countable spaces can be found here.
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $3$: Continuity generalized: topological spaces: $3.2$: Bases: Example $3.2.7$
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Countability Properties
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $3$: Compactness: Countability Axioms and Separability