A note on rank 2 diagonals

Bella, Angelo; Spadaro, Santi

doi:10.4995/agt.2020.12065

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Cardinal Inequalities1

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2024

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Cited by 5 publications

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“…It is interesting to note that, in the above theorem "cellular-countably compact" cannot be replaced with "cellularity at most continuum (see [6,Theorem 2.3]).…”

Section: Cardinal Inequalitiesmentioning

confidence: 99%

On cellular-countably compact spaces

Singh

2022

Filomat

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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 cellularcountably 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 Erd?s and Rad??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?-diagonal is at most c. Finally, we study the topological behavior of cellular-countably compact spaces on subspaces and products.

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“…It is interesting to note that, in the above theorem "cellular-countably compact" cannot be replaced with "cellularity at most continuum (see [6,Theorem 2.3]).…”

Section: Cardinal Inequalitiesmentioning

confidence: 99%