On the maximal -compactification of products of two -spaces.
On the -invariance property for -flows.
On topological ergodic measure spaces.
On transformation semigroups which are -semigroups.
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.
Order and domains of attraction of control sets in flag manifolds.
Ordering the local subsemigroups of a semigroup.
Parallelizability of Proper Actions, Global K-slices and Maximal Compact Subgroups.
Partial orders and their semigroups of closed relations.
Partial orders, closed relations and their automorphisms.
Periodicity and almost periodicity in Markov lattice semigroups
Principal continuum congruences, regular ...-classes and local subsemigroups.
Problems on Periodicity - Functions and Semigroups
Products of locally compact groups with zero and their actions.
Proper actions of locally compact groups on equivariant absolute extensors
Let G be a locally compact Hausdorff group. We study equivariant absolute (neighborhood) extensors (G-AE's and G-ANE's) in the category G-ℳ of all proper G-spaces that are metrizable by a G-invariant metric. We first solve the linearization problem for proper group actions by proving that each X ∈ G-ℳ admits an equivariant embedding in a Banach G-space L such that L∖{0} is a proper G-space and L∖{0} ∈ G-AE. This implies that in G-ℳ the notions of G-A(N)E and G-A(N)R coincide. Our embedding result...
Properties of a pair of functions which generate a dense subsemigroup of S(X).
Recursions with uniquely determined topologies
Reflexively representable but not Hilbert representable compact flows and semitopological semigroups
We show that for many natural topological groups G (including the group ℤ of integers) there exist compact metric G-spaces (cascades for G = ℤ) which are reflexively representable but not Hilbert representable. This answers a question of T. Downarowicz. The proof is based on a classical example of W. Rudin and its generalizations. A~crucial step in the proof is our recent result which states that every weakly almost periodic function on a compact G-flow X comes from a G-representation of X on reflexive...
Regular ....-classes of semigroups of continua.
Remark on topological spaces with given semigroups