Tychonoff Expansions with Prescribed Resolvability Properties

The recent literature offers examples, specific and hand-crafted, of Tychonoff spaces (in ZFC) which respond negatively to these questions, due respectively to Ceder and Pearson (1967) and to Comfort and Garc\'ia-Ferreira (2001): (1) Is every $\omega$-resolvable space maximally resolvable? (2) Is every maximally resolvable space extraresolvable? Now using the method of ${\mathcal{KID}}$ expansion, the authors show that {\it every} suitably restricted Tychonoff topological space (X,\sT) admits a larger Tychonoff topology (that is, an "expansion") witnessing such failure. Specifically the authors show in ZFC that if (X,\sT) is a maximally resolvable Tychonoff space with S(X,\sT)\leq\Delta(X,\sT)=\kappa, then (X,\sT) has Tychonoff expansions \sU=\sU_i ($1\leq i\leq5$), with \Delta(X,\sU_i)=\Delta(X,\sT) and S(X,\sU_i)\leq\Delta(X,\sU_i), such that (X,\sU_i) is: ($i=1$) $\omega$-resolvable but not maximally resolvable; ($i=2$) [if $\kappa'$ is regular, with S(X,\sT)\leq\kappa'\leq\kappa] $\tau$-resolvable for all $\tau<\kappa'$, but not $\kappa'$-resolvable; ($i=3$) maximally resolvable, but not extraresolvable; ($i=4$) extraresolvable, but not maximally resolvable; ($i=5$) maximally resolvable and extraresolvable, but not strongly extraresolvable.Comment: 25 pages, 0 figure