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Tychonoff expansions by independent families

Author: Wanjun Hu
Journal: Proc. Amer. Math. Soc. 131 (2003), 3607-3616
MSC (2000): Primary 54A25, 05D05; Secondary 54B99
Published electronically: February 24, 2003
MathSciNet review: 1991775
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Abstract: A method for Tychonoff expansions using independent families is introduced. Using this method we prove that every countable Tychonoff space which admits a partition into infinitely many open-hereditarily irresolvable dense subspaces has a Tychonoff expansion that is $\omega$-resolvable but not strongly extraresolvable. We also show that, under Luzin's Hypothesis ( $2^{\omega_1} = 2^\omega$), there exists an $\omega$-resolvable Tychonoff space of size $\omega_1$ which is not maximally resolvable.

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Additional Information

Wanjun Hu
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
Address at time of publication: Department of Mathematics and Computer Science, Albany State University, Albany, Georgia 31705

Keywords: Independent family, KID-expansion, Luzin's Hypothesis, resolvable space
Received by editor(s): October 5, 2001
Received by editor(s) in revised form: June 3, 2002
Published electronically: February 24, 2003
Additional Notes: The author thanks Dr. W.W. Comfort for invaluable guidance in his Ph.D study, and the Mathematics Department of Wesleyan University for generous support
Communicated by: Alan Dow
Article copyright: © Copyright 2003 American Mathematical Society