PlanetMath: residual

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residual

(Definition)

A subspace of a topological space is called residual (or comeager) if and only if it is second category and its complement $X\setminus A$ is first category. Equivalently, a set is residual if and only if it contains a countable intersection of open dense sets.

"residual" is owned by mps. [ full author list (2) | owner history (1) ]

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Also defines:

comeager

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Cross-references: dense sets, intersection, countable, contains, complement, second category, topological space, subspace
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This is version 4 of residual, born on 2002-09-27, modified 2005-10-22.
Object id is 3476, canonical name is Residual.
Accessed 5076 times total.

Classification:

54E52 (General topology :: Spaces with richer structures :: Baire category, Baire spaces)

Pending Errata and Addenda

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