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Abstract: For $\kappa$ a cardinal, a space $X=X,\sT$ is $\kappa$-{\it resolvable} if$X$ admits $\kappa$-many pairwise disjoint $\sT$-dense subsets; $X,\sT$ is{\it exactly} $\kappa$-{\it resolvable} if it is $\kappa$-resolvable but not$\kappa^+$-resolvable.The present paper complements and supplements the authors- earlier work,which showed for suitably restricted spaces $X,\sT$ and cardinals$\kappa\geq\lambda\geq\omega$ that $X,\sT$, if $\kappa$-resolvable, admits anexpansion $\sU\supseteq\sT$, with $X,\sU$ Tychonoff if $X,\sT$ isTychonoff, such that $X,\sU$ is $\mu$-resolvable for all $\mu<\lambda$ but isnot $\lambda$-resolvable cf. Theorem~3.3 of \cite{comfhu10}. Here the -finitecase- is addressed. The authors show in ZFC for $1


Author: W.W. Comfort, Wanjun Hu

Source: https://arxiv.org/



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