Smirnov metrization theorem

The Smirnov metrization theorem establishes necessary and sufficient conditions for a topological spaceMathworldPlanetmath to be metrizable. The theorem reduces questions of metrizability to paracompactness and a local metrizability condition.

Definition: A space X is locally metrizable if every point xX has a neighborhoodMathworldPlanetmathPlanetmath that is metrizable in the subspace topology.

Theorem (Smirnov metrization theorem): A space is metrizable if and only if it is paracompact and locally metrizable.

Title Smirnov metrization theorem
Canonical name SmirnovMetrizationTheorem
Date of creation 2013-03-22 18:01:00
Last modified on 2013-03-22 18:01:00
Owner rm50 (10146)
Last modified by rm50 (10146)
Numerical id 7
Author rm50 (10146)
Entry type Theorem
Classification msc 54E35
Defines locally metrizable