On the division by Rn.
On the embedding theorem
On the exact completion of the homotopy category
On the existence of maps having graphs connected and dense
On the External Characterization of Topological Functors.
On the foundations of Topology
On the functor of order-preserving functionals
We introduce a functor of order-preserving functionals which contains some known functors as subfunctors. It is shown that this functor is weakly normal and generates a monad.
On the fundamental dimension of the Cartesian product of compacta with the fundamental dimension 2
On the Hausdorff Dimension of Topological Subspaces
It is shown that every Polish space X with admits a compact subspace Y such that where and denote the topological and Hausdorff dimensions, respectively.
On the homogeneity of the Tychonoff cube
On the hyperspace
Let be a continuum and a positive integer. Let be the hyperspace of all nonempty closed subsets of with at most components, endowed with the Hausdorff metric. For compact subset of , define the hyperspace . In this paper, we consider the hyperspace , which can be a tool to study the space . We study this hyperspace in the class of finite graphs and in general, we prove some properties such as: aposyndesis, local connectedness, arcwise disconnectedness, and contractibility.
On the hyperspace of bounded closed sets under a generalized Hausdorff stationary fuzzy metric
In this paper, we generalize the classical Hausdorff metric with t-norms and obtain its basic properties. Furthermore, for a given stationary fuzzy metric space with a t-norm without zero divisors, we propose a method for constructing a generalized Hausdorff fuzzy metric on the set of the nonempty bounded closed subsets. Finally we discuss several important properties as completeness, completion and precompactness.
On the hyperspace of subcontinua of a finite graph I
On the hyperspace of subcontinua of a finite graph, II
On the hyperspaces of hereditarily indecomposable continua
On the hyperspaces of snake-like and circle-like continua
On the Lifshits Constant for Hyperspaces
The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < ϰ(X) where ϰ(X) is the so-called Lifshits constant of X. For many spaces we have ϰ(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.
On the locally fine construction in uniform spaces, locales and formal spaces
On the -fold symmetric product of a space with a --property -network (-network)
We study the relation between a space satisfying certain generalized metric properties and its -fold symmetric product satisfying the same properties. We prove that has a --property -network if and only if so does . Moreover, if is regular then has a --property -network if and only if so does . By these results, we obtain that is strict -space (strict -space) if and only if so is .
On the Nachbin compactification of products of totally ordered spaces.