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Resolvable, not maximally resolvable spaces

✍ Scribed by Frederick W Eckertson

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 769 KB
Volume: 79
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(96)00159-9

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✦ Synopsis

The formation of maximal topologies and the use of maximal independent families are the only known techniques for constructing irresolvable spaces. Using side conditions to control maximal constructions, we give a new construction of n-resolvable, not (n + I )-resolvable spaces. In another direction, we use the existence of a crowded, irresolvable, strong P, space to construct infinitely resolvable, not maximally resolvable spaces. Relative to the existence of a measurable cardinal, the latter result answers several longstanding questions in this area. 0 1997 Elsevier Science B.V.

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