The largest proper regular ideal of
The lattice of precompact topologies on .
The Lindelöf property and pseudo--compactness in spaces and topological groups
We introduce and study, following Z. Frol’ık, the class of regular -spaces such that the product is pseudo--compact, for every regular pseudo--compact -space . We show that every pseudo--compact space which is locally is in and that every regular Lindelöf -space belongs to . It is also proved that all pseudo--compact -groups are in . The problem of characterization of subgroups of -factorizable (equivalently, pseudo--compact) -groups is considered as well. We give some necessary...
The local contractibility of the homeomorphism space of a 2-polyhedron
The local weight of an effective locally compact transformation group and the dimension of
The minimum tree for a given zero-entropy period.
The monomorphism semigroup of S(X).
The multicores in metric spaces and their application in fixed point theory
This paper discusses the notion, the properties and the application of multicores, i.e. some compact sets contained in metric spaces.
The nonexistence of expansive homeomorphisms of chainable continua
A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x, y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that . In this paper, we prove that if a homeomorphism f:X → X of a continuum X can be lifted to an onto map h:P → P of the pseudo-arc P, then f is not expansive. As a corollary, we prove that there are no expansive homeomorphisms on chainable continua. This is an affirmative answer to one of Williams’ conjectures.
The nonexistence of expansive homeomorphisms of dendroids
The nonexistence of universal metric flows
We consider dynamical systems of the form where is a compact metric space and is either a continuous map or a homeomorphism and provide a new proof that there is no universal metric dynamical system of this kind. The same is true for metric minimal dynamical systems and for metric abstract -limit sets, answering a question by Will Brian.
The omega limit sets of subsets in a metric space
In this paper, we discuss the properties of limit sets of subsets and attractors in a compact metric space. It is shown that the -limit set of is the limit point of the sequence in and also a quasi-attractor is the limit point of attractors with respect to the Hausdorff metric. It is shown that if a component of an attractor is not an attractor, then it must be a real quasi-attractor.
The open-open topology for function spaces.
The partially ordered collection of regular ...-classes of S(X).
The ping-pong game, geometric entropy and expansiveness for group actions on Peano continua having free dendrites
It is shown that each expansive group action on a Peano continuum having a free dendrite must have a ping-pong game, and has positive geometric entropy when the acting group is finitely generated. As a corollary, it is shown that each Peano continuum having a free dendrite admits no expansive nilpotent group actions.
The quantum double of a (locally) compact group.
The Ramsey sets and related sigma algebras and ideals
The real-analytic solutions of the Abel functional equation
For the Abel equation on a real-analytic manifold a dynamical criterion of solvability in real-analytic functions is proved.
The regular open-open topology for function spaces.
The relationship between algebraic numbers and expansiveness of automorphisms on compact abelian groups