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Based on some earlier findings on Banach Category Theorem for some “nice” -ideals by J. Kaniewski, D. Rose and myself I introduce the operator ( stands for “heavy points”) to refine and generalize kernel constructions of A. H. Stone. Having obtained in this way a generalized Kuratowski’s decomposition theorem I prove some characterizations of the domains of functions having “many” points of -continuity. Results of this type lead, in the case of the -ideal of meager sets, to important statements...
We construct examples of mappings and between locally connected continua such that and are near-homeomorphisms while is not, and is a near-homeomorphism, while and are not. Similar examples for refinable mappings are constructed.
The main purpose of this paper is to introduce the concept of intuitionistic -fuzzy quasi-coincident neighborhood systems of intuitiostic fuzzy points. The relation between the category of intuitionistic -fuzzy topological spaces and the category of intuitionistic -fuzzy quasi-coincident neighborhood spaces are studied. By using fuzzifying topology, the notion of generated intuitionistic -fuzzy topology is proposed, and the connections among generated intuitionistic -fuzzy topological spaces,...
R. A. Johnson showed that there is no translation-invariant Borel lifting for the measure algebra of ℝ/ℤ equipped with Haar measure, a result which was generalized by M. Talagrand to non-discrete locally compact abelian groups and by J. Kupka and K. Prikry to arbitrary non-discrete locally compact groups. In this paper we study analogs of these results for category algebras (the Borel σ-algebra modulo the ideal of first category sets) of topological groups. Our main results are for the class of...
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