Tychonoff expansions by independent families
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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.References
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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
- Email: whu@claude.math.wesleyan.edu, whu@asurams.edu
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3607-3616
- MSC (2000): Primary 54A25, 05D05; Secondary 54B99
- DOI: https://doi.org/10.1090/S0002-9939-03-06660-7
- MathSciNet review: 1991775