On the iterative test for j-contractive mappings in uniform spaces
Edelstein iterative test for j-contractive mappings in uniform spaces is established.
On the Lefschetz fixed point theorem
On the Lyapunov numbers
We introduce and study the Lyapunov numbers-quantitative measures of the sensitivity of a dynamical system (X,f) given by a compact metric space X and a continuous map f: X → X. In particular, we prove that for a minimal topologically weakly mixing system all Lyapunov numbers are the same.
On the maximal -compactification of products of two -spaces.
On the multiple Birkhoff recurrence theorem in dynamics
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 orbits of -closure points of ultimately nonexpansive mappings.
On the Periodic Points of Topological Markov Chains.
On the ∗-product in kneading theory
We discuss a generalization of the *-product in kneading theory to maps with an arbitrary finite number of turning points. This is based on an investigation of the factorization of permutations into products of permutations with some special properties relevant for dynamics on the unit interval.
On the proximate fixed-point property for multifunctions
On the pseudo-processes and pseudo-dynamical systems
On the representation of orthocomplemented posets
On the rotation sets for non-continuous circle maps.
On the -invariance property for -flows.
On the Schauder fixed point theorem
The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.
On the selector problems for the partitions of Polish spaces and for the compact-valued mappings
On the self-similar Jordan arcs admitting structure parametrization.
On the sequential order