Published in Journal of Fixed Point Theory and Applications
In this paper, we present relative retracts and we can say that these are multilevel retracts which either retain given properties depending on the level or not. Some properties are constant and are present on every level. These properties are especially important in regard to the theory of coincidence. The class of relative retracts consists of re...
Let Z, H be spaces. In previous work, we introduced the direct (inclusion) system induced by the set of maps between the spaces Z and H. Its direct limit is a subset of Z × H, but its topology is different from the relative topology. We found that many of the spaces constructed from this method are pseudo-compact and Tychonoff. We are going to show...
Published in Journal of Fixed Point Theory and Applications
The application of the theory of multimorphisms leads to the presentation of a new definition of a multidomination of metric spaces. With the help of this definition we obtain the new properties of multidomination in regard to multicontractibility, path connectedness and locally path connectedness.
Published in Vietnam Journal of Mathematics
The aim of this paper is to show the admissibility and the AR-property of some unbounded convex sets in a class of non-locally convex linear metric spaces.
Published in Forum Mathematicum
We prove that for any closed subgroup H of a locally compact Hausdorff group G the following properties are mutually equivalent: (1) the coset space G/H is locally contractible, (2) G/H is finite-dimensional and locally connected, (3) G/H is a manifold. Assume that G is a locally compact group with compact space of connected components. If the natu...
All spaces here are Tychonoff spaces. The class AE(0) consists of those spaces which are absolute extensors for compact zero-dimensional spaces. We define and study here the subclass AE(0)rp, consisting of those spaces for which extensions of continuous functions can be chosen to have the same range. We prove these results. If each point of T 2 AE(...
Published in Open Mathematics
For a metrizable space X and a finite measure space (Ω, $\mathfrak{M}$, µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of $\mathfrak{M}$-measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. ...
Published in Arabian Journal of Mathematics
This paper reviews the old and new landmark extensions of the famous intermediate value theorem (IVT) of Bolzano and Poincaré to a set-valued operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidema...
Published in Acta Mathematica Sinica, English Series
Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-dimensional absolute retracts. Michigan Math. J., 33, 291–313 (1986)] on strong Z-sets in ANR’s and absorbing sets is generalized to nonseparable case. It is shown that if an ANR X is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and w...
Published in Lobachevskii Journal of Mathematics
In this paper, we introduce and study the notion of almost contra-continuous multifunctions. Characterizations and properties of almost contra-continuous multifunctions are discussed.
