### On the theorems of Y. Mibu and G. Debs on separate continuity.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Back to Simple Search
# Advanced Search

Based on some earlier findings on Banach Category Theorem for some “nice” $\sigma $-ideals by J. Kaniewski, D. Rose and myself I introduce the $h$ operator ($h$ 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 $h$-continuity. Results of this type lead, in the case of the $\sigma $-ideal of meager sets, to important statements...

We explore (weak) continuity properties of group operations. For this purpose, the Novak number and developability number are applied. It is shown that if $(G,\xb7,\tau )$ is a regular right (left) semitopological group with $\mathrm{dev}\left(G\right)<\mathrm{Nov}\left(G\right)$ such that all left (right) translations are feebly continuous, then $(G,\xb7,\tau )$ is a topological group. This extends several results in literature.

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...

A simple machinery is developed for the preservation of Baire spaces under preimages. Subsequently, some properties of maps which preserve nowhere dense sets are given.

**Page 1**