Homogeneous spaces admitting transitive semigroups.
Integral Global Weights for Torus Actions on Projective Spaces.
Invariant metrics on -spaces
Let be a -space such that the orbit space is metrizable. Suppose a family of slices is given at each point of . We study a construction which associates, under some conditions on the family of slices, with any metric on an invariant metric on . We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and locally connected metric space.
Isometry groups of non standard metric products
We consider isometry groups of a fairly general class of non standard products of metric spaces. We present sufficient conditions under which the isometry group of a non standard product of metric spaces splits as a permutation group into direct or wreath product of isometry groups of some metric spaces.
Iteration semigroups with generalized convex, concave and affine elements.
Left zero covering homomorphisms of laminated nearrings.
Lie generators for semigroups of transformations on a Polish space.
Locally Sierpinski Quotients.
Maximal inverse subsemigroups of S(Sn).
Minimal actions of homeomorphism groups
Let X be a closed manifold of dimension 2 or higher or the Hilbert cube. Following Uspenskij one can consider the action of Homeo(X) equipped with the compact-open topology on , the space of maximal chains in , equipped with the Vietoris topology. We show that if one restricts the action to M ⊂ Φ, the space of maximal chains of continua, then the action is minimal but not transitive. Thus one shows that the action of Homeo(X) on , the universal minimal space of Homeo(X), is not transitive (improving...
Minimal and distal functions on semidirect products of groups
Monomorphisms of semigroups of B-rigid local dendrites.
Near-rings of continuous functions on compact abelian groups.
New algebras of functions on topological groups arising from G-spaces
For a topological group G we introduce the algebra SUC(G) of strongly uniformly continuous functions. We show that SUC(G) contains the algebra WAP(G) of weakly almost periodic functions as well as the algebras LE(G) and Asp(G) of locally equicontinuous and Asplund functions respectively. For the Polish groups of order preserving homeomorphisms of the unit interval and of isometries of the Urysohn space of diameter 1, we show that SUC(G) is trivial. We introduce the notion of fixed point on a class...
Noncompact semigroup actions.
Non-constant continuous maps of modifications of topological spaces
Non-locally compact Polish groups and two-sided translates of open sets
This paper is devoted to the following question. Suppose that a Polish group G has the property that some non-empty open subset U is covered by finitely many two-sided translates of every other non-empty open subset of G. Is then G necessarily locally compact? Polish groups which do not have the above property are called strongly non-locally compact. We characterize strongly non-locally compact Polish subgroups of in terms of group actions, and prove that certain natural classes of non-locally...
Notes on compact semigroups with identity.
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...