The characterization of the pointwise limits of the sequences of Świątkowski functions is given. Modifications of Świątkowski property with respect to different topologies finer than the Euclidean topology are discussed.
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...
We give sufficient and necessary conditions to be fulfilled by a filter and an ideal in order that the -quotient space of the -ideal product space preserves -properties () (“in the sense of the Łos theorem”). Tychonoff products, box products and ultraproducts appear as special cases of the general construction.
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.
We show that the product of a compact, sequential space with an hereditarily absolutely countably compact space is hereditarily absolutely countably compact, and further that the product of a compact space of countable tightness with an hereditarily absolutely countably compact -bounded space is hereditarily absolutely countably compact.
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.