Proceedings of the American Mathematical Society

Author(s): Wanjun Hu
Journal: Proc. Amer. Math. Soc. 131 (2003), 3607-3616.
MSC (2000): Primary 54A25, 05D05; Secondary 54B99
Posted: February 24, 2003
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54A25, 05D05, 54B99

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
Email: whu@claude.math.wesleyan.edu, whu@asurams.edu

DOI: 10.1090/S0002-9939-03-06660-7
PII: S 0002-9939(03)06660-7
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
Posted: 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
Copyright of article: Copyright 2003, American Mathematical Society

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