On the multiple Birkhoff recurrence theorem in dynamics
On the -fold symmetric product of a space with a --property -network (-network)
We study the relation between a space satisfying certain generalized metric properties and its -fold symmetric product satisfying the same properties. We prove that has a --property -network if and only if so does . Moreover, if is regular then has a --property -network if and only if so does . By these results, we obtain that is strict -space (strict -space) if and only if so is .
On the Nachbin compactification of products of totally ordered spaces.
On the netweight of subspaces
On the Nielsen fixed point theory for multivalued mappings
We present J. Jezierski's approach to the Nielsen fixed point theory for a broad class of multivalued mappings [Je1]. We also describe some generalizations and different techniques existing in the literature.
On the Noetherian type of topological spaces
The Noetherian type of topological spaces is introduced. Connections between the Noetherian type and other cardinal functions of topological spaces are obtained.
On the non-existence of certain group topologies
Minimal Hausdorff (Baire) group topologies of certain groups of transformations naturally occurring in analysis are studied. The results obtained are subsequently applied to show that, e.g., the homeomorphism groups of the rational and of the irrational numbers carry no Polish group topology. In answer to a question of A. S. Kechris it is shown that the group of Borel automorphisms of ℝ cannot be a Polish group either.
On the non-separable descriptive theory
On the Novák completion of convergence groups
On the Novak number of a hyperspace
An estimate for the Novak number of a hyperspace with the Vietoris topology is given. As a consequence it is shown that this cardinal function can decrease passing from a space to its hyperspace.
On the number of compact subsets in topological groups
On the open mapping theorem
On the open-open game
We modify a game due to Berner and Juhász to get what we call “the open-open game (of length ω)”: a round consists of player I choosing a nonempty open subset of a space X and II choosing a nonempty open subset of I’s choice; I wins if the union of II’s open sets is dense in X, otherwise II wins. This game is of interest for ccc spaces. It can be translated into a game on partial orders (trees and Boolean algebras, for example). We present basic results and various conditions under which I or II...
On the orbits of -closure points of ultimately nonexpansive mappings.
On the Order Type L-valued Relations on L-powersets.
On the paracompactness of frames
Through the study of frame congruences, new characterizations of the paracompactness of frames are obtained.
On the Periodic Points of Topological Markov Chains.
On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor
We extend a theorem of S. Claytor in order to characterize the Peano generalized continua which are embeddable into the 2-sphere. We also give a characterization of the Peano generalized continua which admit closed embeddings in the Euclidean plane.
On the pointwise limits of sequences of Świątkowski functions
The characterization of the pointwise limits of the sequences of Świątkowski functions is given. Modifications of Świątkowski property with respect to different topologies finer than the Euclidean topology are discussed.
On the position of the set of monotone mappings in function spaces