Difference between revisions of "Urysohn Metrization Theorem"

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{{Under Construction}}
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If a [[Topological space|topological space]] $X$ satisfies a certain countability axiom (the second) and a certain [[Separation Axioms|separation axiom]] (the regularity axiom), then $X$ can be imbedded in a [[Metric space|metric space]] and is thus ''metrizable''.<ref>Munkres, James R. Topology, 2015. pg. 187.</ref>
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== Further Reading ==
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* [[Metric space|Metric Spaces]]
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* [[Separation Axioms]]
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* [[Topological space|Topological Spaces]]
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== External Links ==
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* [https://ncatlab.org/nlab/show/Urysohn+metrization+theorem nLab - Urysohn Metrization Theorem]
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* [http://www.math.toronto.edu/ivan/mat327/docs/notes/15-umt.pdf Urysohn's Metrization Theorem - University of Toronto Mathematics (pdf)]
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* [https://math.arizona.edu/~gradprogram/workshops/integration/projects/urysohn.pdf University of Arizona Mathematics (pdf)]
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== References ==
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<references group="references" />
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[[Category:General Topology]]

Latest revision as of 05:05, 1 December 2018

If a topological space $X$ satisfies a certain countability axiom (the second) and a certain separation axiom (the regularity axiom), then $X$ can be imbedded in a metric space and is thus metrizable.[1]

Further Reading

External Links

References

  1. Munkres, James R. Topology, 2015. pg. 187.