Cardinal invariants for C-cross topologies

C-cross topologies are introduced. Modifcations of the Kuratowski-Ulam Theorem are considered. Cardinal invariants add, cof, cov and non with respect to meager or nowhere dense subsets are compared. Remarks on invariants cof(nwdY) are mentioned for dense subspaces Y of X.Comment: 11 page

Inverse Systems and I-Favorable Spaces

A compact space X is I-favorable if, and only if X can be representing as a limit of $\sigma$-complete inverse system of compact metrizable spaces with skeletal bonding maps.Comment: 13 page

Topological spaces with the Freese--Nation property II

The aim of this paper is to study the class of spaces with the FNS property and \pi-\FNS property. We shown that compact spaces with the FNS property for some base consisting of cozero-sets are openly generated spaces and spaces with the \pi-\FNS property are skeletally generated spaces

On open-open games of uncountable length

The aim of this note is to investigate the open-open game of uncountable length. We introduce a cardinal number $\mu(X)$, which says how long the Player I has to play to ensure a victory. It is proved that \su(X)\leq\mu(X)\leq\su(X)^+. We also introduce the class $\mathcal C_\kappa$ of topological spaces that can be represented as the inverse limit of $\kappa$-complete system $\{X_\sigma,\pi^\sigma_\rho,\Sigma\}$ with \w(X_\sigma)\leq\kappa and skeletal bonding maps. It is shown that product of spaces which belong to $\mathcal C_\kappa$ also belongs to this class and $\mu(X)\leq\kappa$ whenever $X\in\mathcal C_\kappa$

Parovicenko spaces with structures

We study an analogue of the Parovicenko property in categories of compact spaces with additional structures. In particular, we present an internal characterization of this property in the class of compact median spaces.Comment: Minor revision, final version, 19 page

The Banach–Mazur game and domain theory

We prove that player α has a winning strategy in the Banach–Mazur game on a space X if and only if X is F-Y countably π-domain representable. We show that Choquet complete spaces are F-Y countably domain representable. We give an example of a space, which is F-Y countably domain representable, but which is not F-Y π-domain representable

Topological spaces with the Freese-Nation property

We give a proposal of generalization of the Freese–Nation property for topological spaces. We introduce a few properties related to Freese–Nation property: FNS; FN; FNS ; FNI. This article presents some relationship between these concepts. We show that spaces with the FNS property satisfy ccc and any product of such spaces also satisfies ccc. We show that all metrizable spaces have the FN property

Distribution of Carex limosa L. and Scheuchzeria palustris L. in Poland

In 1949-1989 483 sites of Carex limosa and 315 sites of Scheuchzeria palustris were recorded in Poland. These plants were described in 16 plant communities of the following classes: Scheuchzerio-Caricetea fuscae, Oxycocco-Sphagnetea and Phragmitetea. Carex limosa and Scheuchzeria palustris occur mostly in the following communities in Poland: Caricetum limosae, Drepanoclado-Caricetum limosae, Sphagno- Caricetum limosae and Caricetum limoso-diandrae.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę