Baire space


Also found in: Wikipedia.

Baire space

[′ber ‚spās]
(mathematics)
A topological space in which every countable intersection of dense, open subsets is dense in the space.
References in periodicals archive ?
Then (X, T) is called a Fuzzy Baire space if int ([[disjunction].
If the Fuzzy topological space (X, T) is a Fuzzy Baire space, then no non-zero Fuzzy open set is a Fuzzy first category set in (X, T).
Hence no non- zero Fuzzy open set in a Fuzzy Baire space is a Fuzzy first category set.
i]'s are Fuzzy dense and Fuzzy open sets in (X, T), then (X, T) is a Fuzzy Baire space.
If (X, T) is a Fuzzy nodec space, then (X, T) is not a Fuzzy Baire space.
If (X, T) is a Fuzzy Baire space, then every non-zero Fuzzy residual set [lambda] in (X, T) contains a Fuzzy [G.
If [lambda] is a Fuzzy first category set in a Fuzzy Baire space (X, T), then there is a non-zero Fuzzy [F.
i])) = int(1) = 1 [not equal to] 0, a contradiction to (X, T) being a Fuzzy Baire space in which int ( [[disconjunction].
j]) = 1-0 = 1, (since (X, T) is a Fuzzy Baire space, int ([[lambda].
If (X, T) is a totally Fuzzy second category, Fuzzy regular space, then (X, T) is a Fuzzy Baire space.
The concepts of Baire spaces have been studied extensively in classical topology in [5], [6], [8] and [9].
Mc Coy, Baire Spaces, Dissertationes Mathematical, 141 (1977), 1-77.