Nagata–Smirnov metrization theorem
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The Nagata–Smirnov metrization theorem in topology characterizes when a topological space is metrizable. The theorem states that a topological space X is metrizable if and only if it is regular and Hausdorff and has a countably locally finite basis.
Unlike Urysohn's metrization theorem, which provides a sufficient condition for metrization, this theorem provides both a necessary and sufficient condition for a topological space to be metrizable.
[edit] See also
[edit] References
- Topology, James R. Munkres, Prentice Hall, 1975. ISBN 0-13-925495-1
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