Smirnov metrization theorem
The Smirnov metrization theorem establishes necessary and sufficient conditions for a topological space
to be metrizable. The theorem reduces questions of metrizability to paracompactness and a local metrizability condition.
Definition: A space is locally metrizable if every point has a neighborhood 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 |