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Topology and its Applications
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Topology and its Applications
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Resolvability properties via independent families

Authors: Comfort, W.W.; Hu, Wanjun;

Resolvability properties via independent families

Abstract

For a given cardinal number \(\kappa > 1\), a topological space \(X\) is said to be \(\kappa\)-resolvable if it contains \(\kappa\) many pairwise disjoint dense subspaces. \(\Delta(X)\)-resolvable spaces are called maximally resolvable; here \(\Delta(X)\) is the dispersion character of \(X\), the minimal cardinality of a non-empty open subset of \(X\). \(X\) is extraresolvable if it contains a collection \(\mathcal D\) of dense subsets with \(| \mathcal D| = \Delta(X)^+\), such that the intersection of any two distinct elements of \(\mathcal D\) is nowhere dense in \(X\). This paper deals with the question of Juhász, Soukup and Szentmiklóssy if every extraresolvable Tychonoff space is maximally resolvable. Using some combinatorial principles the authors show that if GCH fails, there are extraresolvable not maximally resolvable Tychonoff spaces. It is also shown that a dense \(\omega\)-resolvable subspace of \(D(\lambda)^I\) is \(\lambda\)-resolvable.

Related Organizations
Keywords

Consistency and independence results in general topology, Maximally resolvable space, Other combinatorial set theory, independent family, Partitions of sets, extraresolvable space, Extraresolvable space, Independent family, maximally resolvable space, Cardinality properties (cardinal functions and inequalities, discrete subsets), Consistency and independence results, Geometry and Topology, Souslin number, ω-resolvable space, \(\kappa\)-resolvable space

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Average
Top 10%
Average
hybrid