An Ascoli theorem for sequential spaces.
An atomic map onto an arbitrary metric continuum
An Egoroff-type theorem for set-valued measurable functions.
An embedding theorem of infinite-dimensional manifold pairs in the model space
An Equivariant Extension Theorem and G-Retracts with a Finite Structure.
An evaluating characterization of homomorphisms
This work provides an evaluating complete description of positive homomorphisms on an arbitrary algebra of real-valued functions.
An Exactly Two-to-One Map from an Indecomposable Chainable Continuum
It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.
An example concerning automorphisms of generalized cubes
An example for mappings related to confluence
Confluence of a mapping between topological spaces can be defined by several ways. J.J. Charatonik asked if two definitions of the confluence using the components and quasi-components are equivalent for surjective mappings with compact point inverses. We give the negative answer to this question in Example 2.1.
An example for mappings related to semi-confluence.
An example of 2-dimensional quasihomeomorphic sets
An example of a space whose all continuous mappings are almost injective
We show that all continuous maps of a space onto second countable spaces are pseudo-open if and only if every discrete family of nonempty -subsets of is finite. We also prove under CH that there exists a dense subspace of the real line , such that every continuous map of is almost injective and cannot be represented as , where is compact and is countable. This partially answers a question of V.V. Tkachuk in [Tk]. We show that for a compact , all continuous maps of onto second...
An example of a Ф-algebra whose uniform closure is a ring of continuous functions
An example related to strongly pointwise self-homeomorphic dendrites
Such spaces in which a homeomorphic image of the whole space can be found in every open set are called self-homeomorphic. W.J. Charatonik and A. Dilks posed a problem related to strongly pointwise self-homeomorphic dendrites. We solve this problem negatively in Example 2.1.
An existence theorem via an intuitive idea and fixed-point theorems
An extension theorem for continuous functions
An extension theorem for multifunctions and a characterization of complete metric spaces
An extension theorem for separately continuous functions and its application to functional analysis
An implicit-function theorem for a class of monotone generalized equations
An independency result in connectification theory
A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let be the following statement: “a perfect -space with no more than clopen subsets is connectifiable if and only if no proper nonempty clopen subset of is feebly compact". In this note we show that neither nor is provable in ZFC.