Geodesic
On cellular-countably compact spaces
Filomat, Tome 36 (2022) no. 5, p. 1469

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DOI

A space X is said to be cellular-countably compact if for each cellular family U in X, there is a countably compact subspace K of X such that U ∩ K ∅ for each U ∈ U. The class of cellular-countably compact spaces contain the classes of countably compact spaces and cellular-compact spaces and contained in a class of pseudocompact spaces. We give an example of Tychonoff DCCC space which is not cellular-countably compact. By using Erdȍs and Radó's theorem, we establish the cardinal inequalities for cellular-countably compact spaces. We show that the cardinality of a normal cellular-countably compact space with a G δ-diagonal is at most c. Finally, we study the topological behavior of cellular-countably compact spaces on subspaces and products.
DOI : 10.2298/FIL2205469S
Classification : 54D20, 54E35, 54D55, 54D99
Keywords: Cellular-countably copmpact, cellular-compact, cellular-Lindel öf, ccc, covering, first countable, topological space 
Sumit Singh. On cellular-countably compact spaces. Filomat, Tome 36 (2022) no. 5, p. 1469 . doi: 10.2298/FIL2205469S
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     doi = {10.2298/FIL2205469S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2205469S/}
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