263 research outputs found
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 Professorâs 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 PolonistĂłw â Henryk Markiewicz
Great teacher of Polish philologists â 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 Professorâs 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
- âŠ