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On the preservation of Baire and weakly Baire category

Alireza Kamel Mirmostafaee, Zbigniew Piotrowski (2016)

Mathematica Bohemica

We consider the question of preservation of Baire and weakly Baire category under images and preimages of certain kind of functions. It is known that Baire category is preserved under image of quasi-continuous feebly open surjections. In order to extend this result, we introduce a strictly larger class of quasi-continuous functions, i.e. the class of quasi-interior continuous functions. We show that Baire and weakly Baire categories are preserved under image of feebly open quasi-interior continuous...

On the preservation of separation axioms in products

Milan Z. Grulović, Miloš S. Kurilić (1992)

Commentationes Mathematicae Universitatis Carolinae

We give sufficient and necessary conditions to be fulfilled by a filter Ψ and an ideal Λ in order that the Ψ -quotient space of the Λ -ideal product space preserves T k -properties ( k = 0 , 1 , 2 , 3 , 3 1 2 ) (“in the sense of the Łos theorem”). Tychonoff products, box products and ultraproducts appear as special cases of the general construction.

On the ∗-product in kneading theory

Karen Brucks, R. Galeeva, P. Mumbrú, D. Rockmore, Charles Tresser (1997)

Fundamenta Mathematicae

We discuss a generalization of the *-product in kneading theory to maps with an arbitrary finite number of turning points. This is based on an investigation of the factorization of permutations into products of permutations with some special properties relevant for dynamics on the unit interval.

On the product of a compact space with an hereditarily absolutely countably compact space

Maddalena Bonanzinga (1997)

Commentationes Mathematicae Universitatis Carolinae

We show that the product of a compact, sequential T 2 space with an hereditarily absolutely countably compact T 3 space is hereditarily absolutely countably compact, and further that the product of a compact T 2 space of countable tightness with an hereditarily absolutely countably compact ω -bounded T 3 space is hereditarily absolutely countably compact.

On the quantification of uniform properties

Robert Lowen, Bart Windels (1997)

Commentationes Mathematicae Universitatis Carolinae

Approach spaces ([4], [5]) turned out to be a natural setting for the quantification of topological properties. Thus a measure of compactness for approach spaces generalizing the well-known Kuratowski measure of non-compactness for metric spaces was defined ([3]). This article shows that approach uniformities (introduced in [6]) have the same advantage with respect to uniform concepts: they allow a nice quantification of uniform properties, such as total boundedness and completeness.

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