Tychonoff expansions by independent families

Hu, Wanjun

doi:10.1090/S0002-9939-03-06660-7

Tychonoff expansions by independent families
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by Wanjun Hu

Proc. Amer. Math. Soc. 131 (2003), 3607-3616

DOI: https://doi.org/10.1090/S0002-9939-03-06660-7

Published electronically: 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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