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Displaying similar documents to “On AP spaces in concern with compact-like sets and submaximality”

A note on transitively D -spaces

Liang-Xue Peng (2011)

Czechoslovak Mathematical Journal

Similarity:

In this note, we show that if for any transitive neighborhood assignment φ for X there is a point-countable refinement such that for any non-closed subset A of X there is some V such that | V A | ω , then X is transitively D . As a corollary, if X is a sequential space and has a point-countable w c s * -network then X is transitively D , and hence if X is a Hausdorff k -space and has a point-countable k -network, then X is transitively D . We prove that if X is a countably compact sequential space and...

p -sequential like properties in function spaces

Salvador García-Ferreira, Angel Tamariz-Mascarúa (1994)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We introduce the properties of a space to be strictly WFU ( M ) or strictly SFU ( M ) , where M ω * , and we analyze them and other generalizations of p -sequentiality ( p ω * ) in Function Spaces, such as Kombarov’s weakly and strongly M -sequentiality, and Kocinac’s WFU ( M ) and SFU ( M ) -properties. We characterize these in C π ( X ) in terms of cover-properties in X ; and we prove that weak M -sequentiality is equivalent to WFU ( L ( M ) ) -property, where L ( M ) = { λ p : λ < ω 1 and p M } , in the class of spaces which are p -compact for every p M ω * ; and that C π ( X ) is a WFU ( L ( M ) ) -space iff...