Scattered compactification for the Arens’ space
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M. Jayachandran, M. Rajagopalan (1977)
Fundamenta Mathematicae
Telgársky, R. (1977)
Abstracta. 5th Winter School on Abstract Analysis
Ziqin Feng (2021)
Commentationes Mathematicae Universitatis Carolinae
We say that a collection of subsets of has property if there is a set and point-countable collections of closed subsets of such that for any there is a finite subcollection of such that . Then we prove that any compact space is Corson if and only if it has a point-- base. A characterization of Corson compacta in terms of (strong) point network is also given. This provides an answer to an open question in “A Biased View of Topology as a Tool in Functional Analysis” (2014) by...
Oleh R. Nykyforchyn (1997)
Commentationes Mathematicae Universitatis Carolinae
We define and investigate a generalization of the notion of convex compacta. Namely, for semiconvex combination in a semiconvex compactum we allow the existence of non-trivial loops connecting a point with itself. It is proved that any semiconvex compactum contains two non-empty convex compacta, the center and the weak center. The center is the largest compactum such that semiconvex combination induces a convex structure on it. The convex structure on the weak center does not necessarily coincide...
Angelo Bella, Peter Nyikos (2010)
Colloquium Mathematicae
The general question of when a countably compact topological space is sequentially compact, or has a nontrivial convergent sequence, is studied from the viewpoint of basic cardinal invariants and small uncountable cardinals. It is shown that the small uncountable cardinal 𝔥 is both the least cardinality and the least net weight of a countably compact space that is not sequentially compact, and that it is also the least hereditary Lindelöf degree in most published models. Similar results, some definitive,...
Mohammad Ismail, Andrzej Szymański (1993)
Commentationes Mathematicae Universitatis Carolinae
We present short and elementary proofs of the following two known theorems in General Topology: (i) [H. Wicke and J. Worrell] A weakly -refinable countably compact space is compact. (ii) [A. Ostaszewski] A compact Hausdorff space which is a countable union of metrizable spaces is sequential.
Alan S. Dow, Stephen W. Watson (1990)
Commentationes Mathematicae Universitatis Carolinae
D. Guerrero Sánchez, Vladimir Vladimirovich Tkachuk (2017)
Commentationes Mathematicae Universitatis Carolinae
Given a subbase of a space , the game is defined for two players and who respectively pick, at the -th move, a point and a set such that . The game stops after the moves have been made and the player wins if ; otherwise is the winner. Since is an evident modification of the well-known point-open game , the primary line of research is to describe the relationship between and for a given subbase . It turns out that, for any subbase , the player has a winning strategy...
Teklehaimanot Retta (1993)
Czechoslovak Mathematical Journal
Takesi Isiwata (1964)
Czechoslovak Mathematical Journal
Iv. Prodanov (1977)
Mathematische Annalen
Robert L. Blair (1983)
Commentationes Mathematicae Universitatis Carolinae
Guo-Fang Zhang (2008)
Czechoslovak Mathematical Journal
In this paper, we study some properties of relatively strong pseudocompactness and mainly show that if a Tychonoff space and a subspace satisfy that and is strongly pseudocompact and metacompact in , then is compact in . We also give an example to demonstrate that the condition can not be omitted.
Takesi Isiwata (1974)
Fundamenta Mathematicae
J. Bell (1988)
Fundamenta Mathematicae
K. Alster (1979)
Fundamenta Mathematicae
Luciano Stramaccia (1989)
Commentationes Mathematicae Universitatis Carolinae
Salvador García-Ferreira, Manuel Sanchis, Stephen W. Watson (2000)
Czechoslovak Mathematical Journal
For a cardinal , we say that a subset of a space is -compact in if for every continuous function , is a compact subset of . If is a -compact subset of a space , then denotes the degree of -compactness of in . A space is called -pseudocompact if is -compact into itself. For each cardinal , we give an example of an -pseudocompact space such that is not pseudocompact: this answers a question posed by T. Retta in “Some cardinal generalizations of pseudocompactness”...
Oleg Okunev, Angel Tamariz-Mascarúa (2000)
Commentationes Mathematicae Universitatis Carolinae
A space is truly weakly pseudocompact if is either weakly pseudocompact or Lindelöf locally compact. We prove: (1) every locally weakly pseudocompact space is truly weakly pseudocompact if it is either a generalized linearly ordered space, or a proto-metrizable zero-dimensional space with for every ; (2) every locally bounded space is truly weakly pseudocompact; (3) for , the -Lindelöfication of a discrete space of cardinality is weakly pseudocompact if .
Shinji Kawaguchi (2007)
Commentationes Mathematicae Universitatis Carolinae
Arhangel’skii [Sci. Math. Jpn. 55 (2002), 153–201] defined notions of relative paracompactness in terms of locally finite open partial refinement and asked if one can generalize the notions above to the well known Michael’s criteria of paracompactness in [17] and [18]. In this paper, we consider some versions of relative paracompactness defined by locally finite (not necessarily open) partial refinement or locally finite closed partial refinement, and also consider closure-preserving cases, such...
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