PlanetMath: Cantor space

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Cantor space

(Definition)

The Cantor space, denoted by $\mathbb{C}$ is the set of all infinite binary sequences with the product topology. It is a perfect Polish space. It is a compact subspace of the Baire space, the set of all infinite sequences of integers (again with the natural product topology).

References.

Moschovakis, Yiannis N. Descriptive Set Theory. North-Holland Pub. Co. 1980, Amsterdam; New York.

"Cantor space" is owned by mathcam. [ full author list (2) | owner history (1) ]

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Keywords:

Cantor, Polish space, binary sequence, language

Attachments:: uncountable Polish spaces contain Cantor space (Theorem) by gel

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Cross-references: integers, Baire space, subspace, compact, Polish space, perfect, product topology, sequences, binary, infinite
There are 4 references to this entry.

This is version 11 of Cantor space, born on 2003-07-10, modified 2005-03-18.
Object id is 4439, canonical name is CantorSpace.
Accessed 3407 times total.

Classification:

54E50 (General topology :: Spaces with richer structures :: Complete metric spaces)

Pending Errata and Addenda

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