Countably compact spaces admitting full r-skeletons are proximal

2021 ◽  
pp. 107733
Author(s):  
F. Hernández-Hernández ◽  
R. Rojas-Hernández
Keyword(s):  
Compact Spaces ◽  
Countably Compact ◽  
Countably Compact Spaces

Selections and countable compactness

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
David Buhagiar ◽  
Valentin Gutev
Keyword(s):  
Compact Spaces ◽  
Countably Compact ◽  
Countably Compact Spaces ◽  
Countable Compactness

AbstractThe present paper deals with continuous extreme-like selections for the Vietoris hyperspace of countably compact spaces. Several new results and applications are established, along with some known results which are obtained under minimal hypotheses. The paper contains also a number of examples clarifying the role of countable compactness.

scholarly journals Minimal sequential Hausdorff spaces

2004 ◽  
Vol 2004 (22) ◽  
pp. 1169-1177
Author(s):  
Bhamini M. P. Nayar
Keyword(s):  
Hausdorff Spaces ◽  
Sequential Space ◽  
Compact Spaces ◽  
Countably Compact ◽  
Countably Compact Spaces ◽  
Sequential Spaces ◽  
By Products

A sequential space(X,T)is called minimal sequential if no sequential topology onXis strictly weaker thanT. This paper begins the study of minimal sequential Hausdorff spaces. Characterizations of minimal sequential Hausdorff spaces are obtained using filter bases, sequences, and functions satisfying certain graph conditions. Relationships between this class of spaces and other classes of spaces, for example, minimal Hausdorff spaces, countably compact spaces, H-closed spaces, SQ-closed spaces, and subspaces of minimal sequential spaces, are investigated. While the property of being sequential is not (in general) preserved by products, some information is provided on the question of when the product of minimal sequential spaces is minimal sequential.

scholarly journals Maximal topologies

1973 ◽  
Vol 15 (3) ◽  
pp. 279-290 ◽  
Author(s):  
Asit Baran Raha
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Compact Spaces ◽  
Other Hand ◽  
Countably Compact ◽  
Countably Compact Spaces ◽  
Necessary And Sufficient

This article is devoted to studying maximal π spaces where π = Lindelöf, countably compact, connected, lightly compact or pseudocompact. Necessary and sufficient conditions for Lindelöf or countably compact spaces to be maximal Lindelöf or maximal countably compact have been obtained. On the other hand only necessary conditions for maximal π spaces have been deduced where π = connected, lightly compact or pseudocompact.

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