Generalized Radon spaces which are not Radon.
Generalized recurrence, compactifications, and the Lyapunov topology
We study generalized recurrence for closed relations on locally compact spaces. This includes continuous maps and real flows. The main tools are Lyapunov functions and their compactifications. Under certain conditions it is shown that the Lyapunov functions determine the topology of the space.
Generalized Sierpinski sets.
Generic chaos
Generic power series on subsets of the unit disk
We examine the boundary behaviour of the generic power series with coefficients chosen from a fixed bounded set in the sense of Baire category. Notably, we prove that for any open subset of the unit disk with a nonreal boundary point on the unit circle, is a dense set of . As it is demonstrated, this conclusion does not necessarily hold for arbitrary open sets accumulating to the unit circle. To complement these results, a characterization of coefficient sets having this property is given....
Generic Properties of Invariant Measures for Continous Piecewise Monotonic Transformations.
Global attractivity results for mixed-monotone mappings in partially ordered complete metric spaces.
Graphs and common fixed point theorems for sequences of maps.
Green's L-relation for semigroups and compactifications.
Green's L-relation for semigroups and compactifications. (Short Communication).
Green's relations, the V relation and congruences on S(X).
Gregus-type common fixed point theorems for tangential multivalued mappings of integral type in metric spaces.
Group reflection and precompact paratopological groups
We construct a precompact completely regular paratopological Abelian group G of size (2ω)+ such that all subsets of G of cardinality ≤ 2ω are closed. This shows that Protasov’s theorem on non-closed discrete subsets of precompact topological groups cannot be extended to paratopological groups. We also prove that the group reflection of the product of an arbitrary family of paratopological (even semitopological) groups is topologically isomorphic to the product of the group reflections of the factors,...
Group Structures and Rectifiability in Powers of Spaces
We prove that if some power of a space X is rectifiable, then is rectifiable. It follows that no power of the Sorgenfrey line is a topological group and this answers a question of Arhangel’skiĭ. We also show that in Mal’tsev spaces of point-countable type, character and π-character coincide.
Groups acting on covering spaces
Groups associated with minimal flows
Let be topological semigroup, we consider an appropriate semigroup compactification of . In this paper we study the connection between subgroups of a maximal group in a minimal left ideal of , which arise as equivalence classes of some closed left congruence, and the minimal flow characterized by the left congruence. A particular topology is defined on a maximal group and it is shown that a closed subgroup under this topology is precisely the intersection of an equivalence class with the maximal...
Groups of homeomorphisms and normal subgroups of the group of permutations.
Gyration numbers for involutions of subshifts of finite type II.
Gyration numbers for involutions of subshifts of finite type I.