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Nowhere dense subsets and Booth's Lemma

Viacheslav I. Malykhin (1996)

Commentationes Mathematicae Universitatis Carolinae

The following statement is proved to be independent from [ LB + ¬ CH ] : ( * ) Let X be a Tychonoff space with c ( X ) 0 and π w ( X ) < . Then a union of less than of nowhere dense subsets of X is a union of not greater than π w ( X ) of nowhere dense subsets.

Observations on spaces with zeroset or regular G δ -diagonals

Raushan Z. Buzyakova (2005)

Commentationes Mathematicae Universitatis Carolinae

We show that if X 2 has countable extent and X has a zeroset diagonal then X is submetrizable. We also make a couple of observations regarding spaces with a regular G δ -diagonal.

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