The decomposition of functions of bounded ϰ-variation into differences of ϰ-decreasing functions
The Freudenthal space for approximate systems of compacta and some applications.
In this paper we define a space σ(X) for approximate systems of compact spaces. The construction is due to H. Freudenthal for usual inverse sequences [4, p. 153–156]. We establish the following properties of this space: (1) The space σ(X) is a paracompact space, (2) Moreover, if X is an approximate sequence of compact (metric) spaces, then σ(X) is a compact (metric) space (Lemma 2.4). We give the following applications of the space σ(X): (3) If X is an approximate system of continua, then X = limX...
The LCC-topology on the space of continuous functions
The number of metrizable spaces
The structure of compacta satisfying dim(X×X) < 2dimX
The topological structure of adherences of regular languages
Three questions of Borsuk concerning movability and fundamental retraction
Trees of manifolds with boundary
We introduce two new classes of compacta, called trees of manifolds with boundary and boundary trees of manifolds with boundary. We establish their basic properties.
Trivial bundles of spaces of probability measures and countable-dimensionality
The probability measure functor P carries open continuous mappings of compact metric spaces into Q-bundles provided Y is countable-dimensional and all fibers are infinite. This answers a question raised by V. Fedorchuk.
True preimages of compact or separable sets for functional analysts
We discuss various results on the existence of ‘true’ preimages under continuous open maps between -spaces, -lattices and some other spaces. The aim of the paper is to provide accessible proofs of this sort of results for functional-analysts.
Two problems on doubling measures.
Doubling measures appear in relation to quasiconformal mappings of the unit disk of the complex plane onto itself. Each such map determines a homeomorphism of the unit circle on itself, and the problem arises, which mappings f can occur as boundary mappings?