On composants of the bucket handle
On constructive versions of the Tychonoff and Schauder fixed point theorems.
On continuity of measurable group representations and homomorphisms
Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space ℒ(H) of bounded linear operators on H with the weak operator topology. We prove that if U is a measurable map from G to ℒ(H) then it is continuous. This result was known before for separable H. We also prove that the following statement is consistent with ZFC: every measurable homomorphism from a locally compact group into any topological group is continuous.
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 contraction mappings
On contractive mappings in metric spaces
On Convergence Of Certain Sequences And Some Applications II
On convergence of successive approximations of some generalized contraction mappings
On convergence theory in fuzzy topological spaces and its applications
In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the -relation and the -neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong -compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar...
On convergent sequences and fixed point theorems in -metric spaces.
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 countable families of sets without the Baire property
We suggest a method of constructing decompositions of a topological space X having an open subset homeomorphic to the space (ℝⁿ,τ), where n is an integer ≥ 1 and τ is any admissible extension of the Euclidean topology of ℝⁿ (in particular, X can be a finite-dimensional separable metrizable manifold), into a countable family ℱ of sets (dense in X and zero-dimensional in the case of manifolds) such that the union of each non-empty proper subfamily of ℱ does not have the Baire property in X.
On coupled random fixed point results in partially ordered metric spaces
On coverings in the lattice of all group topologies of arbitrary Abelian groups.
On D-connected sets in the space
On decomposing the plane into connected or one-to-one curves
On dense subspaces satisfying stronger separation axioms
We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of -weight less than has a dense completely Hausdorff (and hence Urysohn) subspace. We show that...
On density modulo 1 of some expressions containing algebraic integers
On dimension of locally pseudocompact groups and their quotients
On Dimensional Functions and Topological Markov Chains.