Free products of topological groups with equal uniformities, I
Free products of topological groups with equal uniformities, II
Free uniform measures
Free uniform measures on subinversion-closed spaces
Function Lipschitzian mappings on convex metric spaces
Functional characterizations of p-spaces
We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.
Functional separation of inductive limits and representation of presheaves by sections. Part one: Separation theorems for inductive limits of closured presheaves
Functions and Baire spaces
Functor of extension of -isometric maps between central subsets of the unbounded Urysohn universal space
The aim of the paper is to prove that in the unbounded Urysohn universal space there is a functor of extension of -isometric maps (i.e. dilations) between central subsets of to -isometric maps acting on the whole space. Special properties of the functor are established. It is also shown that the multiplicative group acts continuously on by -isometries.
Further characterizations of boundedly UC spaces
Following the paper [BDC1], further relations between the classical topologies on function spaces and new ones induced by hyperspace topologies on graphs of functions are introduced and further characterizations of boundedly spaces are given.
Further note on Fréchet spaces
Further properties of 1-sequence-covering maps
Some relationships between -sequence-covering maps and weak-open maps or sequence-covering -maps are discussed. These results are used to generalize a result from Lin S., Yan P., Sequence-covering maps of metric spaces, Topology Appl. 109 (2001), 301–314.
Further theory and applications of covering dimension of uniform spaces
Fuzziness and fuzzy equality
Fuzzy distances
In the paper, three different ways of constructing distances between vaguely described objects are shown: a generalization of the classic distance between subsets of a metric space, distance between membership functions of fuzzy sets and a fuzzy metric introduced by generalizing a metric space to fuzzy-metric one. Fuzzy metric spaces defined by Zadeh’s extension principle, particularly to are dealt with in detail.
Fuzzy metrics and statistical metric spaces
Fuzzy neighborhood structures on partially ordered groups.
-metrizable spaces and the images of semi-metric spaces
In this paper, we prove that a space is a -metrizable space if and only if is a weak-open, and -image of a semi-metric space, if and only if is a strong sequence-covering, quotient, and -image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.
Galois spaces, representable spaces and strongly locally homogeneous spaces
Gated sets in metric spaces.