We prove a fixed point theorem for Borsuk continuous mappings with spherical values, which extends a previous result. We apply some nonstandard properties of the Stiefel-Whitney classes.
This work provides an evaluating complete description of positive homomorphisms on an arbitrary algebra of real-valued functions.
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.
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.
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...
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.