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Noncommutative Valdivia compacta

Marek Cúth (2014)

Commentationes Mathematicae Universitatis Carolinae

We prove some generalizations of results concerning Valdivia compact spaces (equivalently spaces with a commutative retractional skeleton) to the spaces with a retractional skeleton (not necessarily commutative). Namely, we show that the dual unit ball of a Banach space is Corson provided the dual unit ball of every equivalent norm has a retractional skeleton. Another result to be mentioned is the following. Having a compact space K , we show that K is Corson if and only if every continuous image...

Nonnormality of remainders of some topological groups

Aleksander V. Arhangel'skii, J. van Mill (2016)

Commentationes Mathematicae Universitatis Carolinae

It is known that every remainder of a topological group is Lindelöf or pseudocompact. Motivated by this result, we study in this paper when a topological group G has a normal remainder. In a previous paper we showed that under mild conditions on G , the Continuum Hypothesis implies that if the Čech-Stone remainder G * of G is normal, then it is Lindelöf. Here we continue this line of investigation, mainly for the case of precompact groups. We show that no pseudocompact group, whose weight is uncountable...

Non-normality points and nice spaces

Sergei Logunov (2021)

Commentationes Mathematicae Universitatis Carolinae

J. Terasawa in " β X - { p } are non-normal for non-discrete spaces X " (2007) and the author in “On non-normality points and metrizable crowded spaces” (2007), independently showed for any metrizable crowded space X that each point p of its Čech–Stone remainder X * is a non-normality point of β X . We introduce a new class of spaces, named nice spaces, which contains both of Sorgenfrey line and every metrizable crowded space. We obtain the result above for every nice space.

Nonnormality points of βX∖X

William Fleissner, Lynne Yengulalp (2011)

Fundamenta Mathematicae

Let X be a crowded metric space of weight κ that is either κ ω -like or locally compact. Let y ∈ βX∖X and assume GCH. Then a space of nonuniform ultrafilters embeds as a closed subspace of (βX∖X)∖y with y as the unique limit point. If, in addition, y is a regular z-ultrafilter, then the space of nonuniform ultrafilters is not normal, and hence (βX∖X)∖y is not normal.

Non-separating subcontinua of planar continua

D. Daniel, C. Islas, R. Leonel, E. D. Tymchatyn (2015)

Colloquium Mathematicae

We revisit an old question of Knaster by demonstrating that each non-degenerate plane hereditarily unicoherent continuum X contains a proper, non-degenerate subcontinuum which does not separate X.

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