We prove that for every Borel ideal, the ideal limits of sequences of continuous functions on
a Polish space are of Baire class one if and only if the ideal does not contain a copy of Fin× …

Abstract top We consider two situations which relate properties of filters with properties of the
limit operators with respect to these filters. In the first one, we show that the space of …

Abstract\We first prove that given any analytic filter ${\cal F} $ on $\omega $ the set of all
functions $ f $ on ${\bf 2}^\omega $ which can be represented as the pointwise limit relative …

We investigate non-separable Banach spaces whose norm-open sets are countable unions
of sets closed in the weak topology and a narrower class of Banach spaces with a network …

In this paper we study a new ideal WR. The main result is the following: an ideal is not
weakly Ramsey if and only if it is above WR in the Katětov order. Weak Ramseyness was …

An internal characterization of metric spaces which are absolute Borel sets of multiplicative
classes is given. This characterization uses complete sequences of covers, a notion …

We discuss three problems of Koszmider on the structure of the spaces of continuous
functions on the Stone compact KA generated by an almost disjoint family A of infinite …

We extend the results of Gul'ko and Sokolov proving that a filter F on ω, regarded as a
subspace of the Cantor set 2ω, is a hereditary Baire space if and only if F is a nonmeager …

We consider the class of compact spaces $ K_A $ which are modifications of the well known
double arrow space. The space $ K_A $ is obtained from a closed subset $ K $ of the unit …

A condensation is a one-to-one onto mapping. It is established that, for each $\sigma $-
compact metrizable space $ X $, the space $ C_ {p}(X) $ of real-valued continuous functions …