On 1/2-homogeneous ANR spaces
On a compactification of the homeomorphism group of the pseudo-arc
A continuum means a compact connected metric space. For a continuum X, H(X) denotes the space of all homeomorphisms of X with the compact-open topology. It is well known that H(X) is a completely metrizable, separable topological group. J. Kennedy [8] considered a compactification of H(X) and studied its properties when X has various types of homogeneity. In this paper we are concerned with the compactification of the homeomorphism group of the pseudo-arc P, which is obtained by the method of...
On a Dimension for a Class of Homeomorphism Groups.
On a problem of Freudenthal's
On a universality property of some abelian Polish groups
We show that every abelian Polish group is the topological factor group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.
On Almost-Tractable Spaces I
On almost-tractable spaces I.
On cardinalities of row spaces of Boolean matrices.
On compactification lattices of subsemigroups of .
On continuous actions commutingwith actions of positive entropy
Let F and G be finitely generated groups of polynomial growth with the degrees of polynomial growth d(F) and d(G) respectively. Let be a continuous action of F on a compact metric space X with a positive topological entropy h(S). Then (i) there are no expansive continuous actions of G on X commuting with S if d(G)
On countable dense and strong n-homogeneity
We prove that if a space X is countable dense homogeneous and no set of size n-1 separates it, then X is strongly n-homogeneous. Our main result is the construction of an example of a Polish space X that is strongly n-homogeneous for every n, but not countable dense homogeneous.
On D-connected sets in the space
On endomorphism semigroups of a fuzzily structured set
On locally Lipschitz locally compact transformation groups of manifolds
In this paper we show that a “locally Lipschitz” locally compact transformation group acting continuously and effectively on a connected paracompact locally Euclidean topological manifold is a Lie group. This is a contribution to the proof of the Hilbert-Smith conjecture. It generalizes the classical Bochner-Montgomery-Kuranishi Theorem[1, 9] and also the Repovš-Ščepin Theorem [17] which holds only for Riemannian manifolds.
On quasi-transitive semigroup actions.
On semigroups of continuous transformations on fuzzily structured sets.
On some minimal transformations of compact spaces
On the Bohr Compactification of a Transformation Group.
On the group of isometries of the Urysohn universal metric space
On the group of isometries on a locally compact metric space.