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representation theorem for compact metric spaces (Theorem)
Theorem   Every compact metric space is a continuous image of the Cantor set.

Bibliography

1
S. Willard, General Topology, Addison-Wesley, Publishing Company, 1970.




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See Also: dimension, Cantor set, Hahn-Mazurkiewicz theorem

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Cross-references: Cantor set, image, continuous, metric space, compact

This is version 5 of representation theorem for compact metric spaces, born on 2004-10-01, modified 2007-05-26.
Object id is 6265, canonical name is RepresentationTheoremForCompactMetricSpaces.
Accessed 1612 times total.

Classification:
AMS MSC54D30 (General topology :: Fairly general properties :: Compactness)
 54E35 (General topology :: Spaces with richer structures :: Metric spaces, metrizability)

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