Exactly n-resolvable topological expansions
Copyright policy )Exactly n-resolvable topological expansions
For $κ$ a cardinal, a space $X=(X,\sT)$ is $κ$-{\it resolvable} if $X$ admits $κ$-many pairwise disjoint $\sT$-dense subsets; $(X,\sT)$ is {\it exactly} $κ$-{\it resolvable} if it is $κ$-resolvable but not $κ^+$-resolvable. The present paper complements and supplements the authors' earlier work, which showed for suitably restricted spaces $(X,\sT)$ and cardinals $κ\geqλ\geqω$ that $(X,\sT)$, if $κ$-resolvable, admits an expansion $\sU\supseteq\sT$, with $(X,\sU)$ Tychonoff if $(X,\sT)$ is Tychonoff, such that $(X,\sU)$ is $μ$-resolvable for all $μ<λ$ but is not $λ$-resolvable (cf. Theorem~3.3 of \cite{comfhu10}). Here the "finite case" is addressed. The authors show in ZFC for $1
- Albany State University United States
- Wesleyan University United States
- State University of New York at Potsdam United States
Several topologies on one set (change of topology, comparison of topologies, lattices of topologies), quasi-regular space, exactly \(n\)-resolvable space, Extremal set theory, General Topology (math.GN), resolvable space, 05A18, 03E05, 54A10, Quasi-regular space, Other combinatorial set theory, Resolvable space, Expansion of topology, expansion of topology, Exactly n-resolvable space, Partitions of sets, n-resolvable space, FOS: Mathematics, Cardinality properties (cardinal functions and inequalities, discrete subsets), Consistency and independence results, Geometry and Topology, \(n\)-resolvable space, Mathematics - General Topology
Several topologies on one set (change of topology, comparison of topologies, lattices of topologies), quasi-regular space, exactly \(n\)-resolvable space, Extremal set theory, General Topology (math.GN), resolvable space, 05A18, 03E05, 54A10, Quasi-regular space, Other combinatorial set theory, Resolvable space, Expansion of topology, expansion of topology, Exactly n-resolvable space, Partitions of sets, n-resolvable space, FOS: Mathematics, Cardinality properties (cardinal functions and inequalities, discrete subsets), Consistency and independence results, Geometry and Topology, \(n\)-resolvable space, Mathematics - General Topology
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