Several fixed point theorems concerning -distance.
Some extensions on the Sadovskii functor.
Some fixed point theorems
Some fixed point theorems for weak contraction conditions of integral type.
Some observations on local uniform boundedness principles
Some problems on Suslin spaces and topological algebras
Some properties of the Hausdorff distance in metric spaces.
Some properties of the Hausdorff distance in complete metric spaces are discussed. Results obtained in this paper explain ideas used in the theory of measures of noncompactness.
Some results on Ciric's quasi-contraction mappings.
Some results on metric trees
Using isometric embedding of metric trees into Banach spaces, this paper will investigate barycenters, type and cotype, and various measures of compactness of metric trees. A metric tree (T, d) is a metric space such that between any two of its points there is a unique arc that is isometric to an interval in ℝ. We begin our investigation by examining isometric embeddings of metric trees into Banach spaces. We then investigate the possible images x₀ = π((x₁ + ... + xₙ)/n), where π is a contractive...
Spaces of ANR's
Spaces of ANR's. II
Stability of convergent continuous descent methods.
Stabilizers of closed sets in the Urysohn space
Building on earlier work of Katětov, Uspenskij proved in [8] that the group of isometries of Urysohn's universal metric space 𝕌, endowed with the pointwise convergence topology, is a universal Polish group (i.e. it contains an isomorphic copy of any Polish group). Answering a question of Gao and Kechris, we prove here the following, more precise result: for any Polish group G, there exists a closed subset F of 𝕌 such that G is topologically isomorphic to the group of isometries of 𝕌 which map...
The Demyanov metric and some other metrics in the family of convex sets
We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.
The dimension of products of complete separable metric spaces
The Kannan's fixed point theorem in a cone rectangular metric space.
The LCC-topology on the space of continuous functions
The number of metrizable spaces
Topological completeness of first countable Hausdorff spaces II
Topological completeness of first countable Hausdorff spaces I