Results 31 to 40 of about 337 (43)

A topological property of β(N)

International Journal of Mathematics and Mathematical Sciences, Volume 3, Issue 4, Page 713-717, 1980., 1980
In this paper we prove that the Stone‐Cech‐compactification of the natural numbers does not admit a countable infinite decomposition into subsets homeomorphic to each other and to the said compactification.
Anastase Nakassis
wiley   +1 more source

Valdivia compact Abelian groups

, 2007
Let R denote the smallest class of compact spaces containing all metric compacta and closed under limits of continuous inverse sequences of retractions. Class R is striclty larger than the class of Valdivia compact spaces.
Kubiś, Wieslaw
core   +3 more sources

Large separated sets of unit vectors in Banach spaces of continuous functions

, 2019
The paper concerns the problem whether a nonseparable $\C(K)$ space must contain a set of unit vectors whose cardinality equals to the density of $\C(K)$ such that the distances between every two distinct vectors are always greater than one.
Cúth, Marek, Kurka, Ondřej, Vejnar, Benjamin   +2 more
core   +1 more source

Means on scattered compacta

, 2013
We prove that a separable Hausdorff topological space $X$ containing a cocountable subset homeomorphic to $[0,\omega_1]$ admits no separately continuous mean operation and no diagonally continuous $n$-mean for $n\ge 2$.Comment: 6 ...
Banakh, Taras, Bonnet, Robert, Kubis, Wieslaw   +2 more
core   +3 more sources

Set-theoretic problems concerning Lindelof spaces [PDF]

, 2010
I survey problems concerning Lindelof spaces which have partial set- theoretic ...
Tall, Franklin D.
core  

The basis problem for subspaces of monotonically normal compacta

, 2016
We prove, assuming Souslin's Hypothesis, that each uncountable subspace of each zero-dimensional monotonically normal compact space contains an uncountable subset of the real line with either the metric, the Sorgenfrey, or the discrete topology.Comment ...
Ahmad Farhat, Baumgartner, Bula, Eisworth, Engelking, Fremlin, Gruenhage, Gruenhage, Gruenhage, Hart, Hocking, Hurewicz, Mardesic, Mazurkiewicz, Nikiel, Nikiel, Ostaszewski, Ostaszewski, Rudin, Rudin, Todorcevic, Todorcevic, Treybig, Treybig   +23 more
core   +1 more source

Base-free Formulas in the Lattice-theoretic Study of Compacta [PDF]

, 2011
The languages of finitary and infinitary logic over the alphabet of bounded lattices have proven to be of considerable use in the study of compacta. Significant among the sentences of these languages are the ones that are base free, those whose truth is ...
Bankston, Paul
core   +1 more source

Metrizability of Clifford topological semigroups

, 2011
We prove that a topological Clifford semigroup $S$ is metrizable if and only if $S$ is an $M$-space and the set $E=\{e\in S:ee=e\}$ of idempotents of $S$ is a metrizable $G_\delta$-set in $S$.
A. Arhangel’skii, A.V. Arkhangel’skiĭ, Alex Ravsky, B. Bokalo, G. Gruenhage, K. Morita, O. Gutik, Oleg Gutik, Oles Potiatynyk, P.D. Kruming, R.J. Koch, T. Banakh, T. Banakh, Taras Banakh   +13 more
core   +1 more source

Reflecting Lindel\"of and converging omega_1-sequences

, 2013
We deal with a conjectured dichotomy for compact Hausdorff spaces: each such space contains a non-trivial converging omega-sequence or a non-trivial converging omega_1-sequence. We establish that this dichotomy holds in a variety of models; these include
Dow, Alan, Hart, Klaas Pieter
core   +1 more source

A class of compact subsets for non-sober topological spaces [PDF]

, 2011
We define a class of subsets of a topological space that coincides with the class of compact saturated subsets when the space is sober, and with enough good properties when the space is not sober.
Poncet, Paul
core