One-to one Carathéodory representation theorem for multifunctions with uncountable values
Only 3-generalized metric spaces have a compatible symmetric topology
We prove that every 3-generalized metric space is metrizable. We also show that for any ʋ with ʋ ≥ 4, not every ʋ-generalized metric space has a compatible symmetric topology.
Open maps between Knaster continua
We investigate the set of open maps from one Knaster continuum to another. A structure theorem for the semigroup of open induced maps on a Knaster continuum is obtained. Homeomorphisms which are not induced are constructed, and it is shown that the induced open maps are dense in the space of open maps between two Knaster continua. Results about the structure of the semigroup of open maps on a Knaster continuum are obtained and two questions about the structure are posed.
Openly factorizable spaces and compact extensions of topological semigroups
We prove that the semigroup operation of a topological semigroup extends to a continuous semigroup operation on its Stone-Čech compactification provided is a pseudocompact openly factorizable space, which means that each map to a second countable space can be written as the composition of an open map onto a second countable space and a map . We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.
Operator and function spaces which are K-analytic
Orbit coupling
Orbit equivalence and Kakutani equivalence with Sturmian subshifts
Using dimension group tools and Bratteli-Vershik representations of minimal Cantor systems we prove that a minimal Cantor system and a Sturmian subshift are topologically conjugate if and only if they are orbit equivalent and Kakutani equivalent.
Order and domains of attraction of control sets in flag manifolds.
Ordered K-theoryand minimal symbolic dynamical systems
Recently a new invariant of K-theoretic nature has emerged which is potentially very useful for the study of symbolic systems. We give an outline of the theory behind this invariant. Then we demonstrate the relevance and power of the invariant, focusing on the families of substitution minimal systems and Toeplitz flows.
Ordered non-Archimedean fuzzy metric spaces and some fixed point results.
Ordering the local subsemigroups of a semigroup.
Ordinals in topological groups
We show that if an uncountable regular cardinal τ and τ + 1 embed in a topological group G as closed subspaces then G is not normal. We also prove that an uncountable regular cardinal cannot be embedded in a torsion free Abelian group that is hereditarily normal. These results are corollaries to our main results about ordinals in topological groups. To state the main results, let τ be an uncountable regular cardinal and G a T₁ topological group. We prove, among others, the following statements:...
Ovals and non-ovoidal Laguerre planes.
-(-) пары расширений минимальных полугрупп преобразований
Parallelizability of Dynamical Systems.
Parallelizability of Proper Actions, Global K-slices and Maximal Compact Subgroups.
Parametric extension of the Poincaré theorem
Parametric general variational-like inequality problem in uniformly smooth Banach space.
Parametrized Cichoń's diagram and small sets
We parametrize Cichoń’s diagram and show how cardinals from Cichoń’s diagram yield classes of small sets of reals. For instance, we show that there exist subsets N and M of and continuous functions such that • N is and , the collection of all vertical sections of N, is a basis for the ideal of measure zero subsets of ; • M is and is a basis for the ideal of meager subsets of ; •. From this we derive that for a separable metric space X, •if for all Borel (resp. ) sets with all...
Paratopological (topological) groups with certain networks
In this paper, we discuss certain networks on paratopological (or topological) groups and give positive or negative answers to the questions in [Lin2013]. We also prove that a non-locally compact, -gentle paratopological group is metrizable if its remainder (in the Hausdorff compactification) is a Fréchet-Urysohn space with a point-countable cs*-network, which improves some theorems in [Liu C., Metrizability of paratopological semitopological groups, Topology Appl. 159 (2012), 1415–1420], [Liu...