Combinatorial images of sets of reals and semifilter trichotomy

Using a dictionary translating a variety of classical and modern covering properties into combinatorial properties of continuous images, we get a simple way to understand the interrelations between these properties in ZFC and in the realm of the trichotomy axiom for upward closed families of sets of natural numbers. While it is now known that the answer to the Hurewicz 1927 problem is positive, it is shown here that semifilter trichotomy implies a negative answer to a slightly weaker form of this problem.Comment: Small update

The combinatorics of Borel covers

In this paper we extend previous studies of selection principles for families of open covers of sets of real numbers to also include families of countable Borel covers. The main results of the paper could be summarized as follows: 1. Some of the classes which were different for open covers are equal for Borel covers -- Section 1; 2. Some Borel classes coincide with classes that have been studied under a different guise by other authors -- Section 4.Comment: Regular updat

Universally Kuratowski-Ulam spaces and open-open games

We examine the class of spaces in which the second player has a winning strategy in the open--open game. We show that this spaces are not universally Kuratowski-Ulam. We also show that the games G and G7 introduced by P. Daniels, K. Kunen, H. Zhou [Fund. Math. 145 (1994), no. 3, 205--220] are not equivalent

The combinatorics of splittability

Marion Scheepers, in his studies of the combinatorics of open covers, introduced the property Split(U,V) asserting that a cover of type U can be split into two covers of type V. In the first part of this paper we give an almost complete classification of all properties of this form where U and V are significant families of covers which appear in the literature (namely, large covers, omega-covers, tau-covers, and gamma-covers), using combinatorial characterizations of these properties in terms related to ultrafilters on N. In the second part of the paper we consider the questions whether, given U and V, the property Split(U,V) is preserved under taking finite unions, arbitrary subsets, powers or products. Several interesting problems remain open.Comment: Small update

Some new directions in infinite-combinatorial topology

We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere are also included, with proofs.Comment: Small update

Great teacher of Polish philologists : Henryk Markiewicz

The author recalls the enormous contributions of Professor Henryk Markiewicz to the development of literacy research in post-war Poland. He emphasises especially organising and composing role of the Professor’s pieces, which constituted the foundations for the systematic knowledge of Polish studies within the scope of the theory of literature. The equally important part was played by prepared by him original anthologies that include the selection of the most important books and articles on literary theory, which present the main streams of the literary research abroad

Wielki Nauczyciel Polonistów – Henryk Markiewicz

Great teacher of Polish philologists – Henryk Markiewicz The author recalls the enormous contributions of Professor Henryk Markiewicz to the development of literacy research in post-war Poland. He emphasises especially organising and composing role of the Professor’s pieces, which constituted the foundations for the systematic knowledge of Polish studies within the scope of the theory of literature. The equally important part was played by prepared by him original anthologies that include the selection of the most important books and articles on literary theory, which present the main streams of the literary research abroad