一般拓扑
We construct, assuming Jensen's principle diamond, a one-dimensional locally connected hereditarily separable continuum without convergent sequences. The construction is an inverse limit in omega_1 steps, and is patterned after the original…
As it was shown in the first part of this paper, there exists a duality between the category DSkeLC (introduced there) and the category SkeLC of locally compact Hausdorff spaces and continuous skeletal maps. We describe here the…
Generalizing Duality Theorem of V. V. Fedorchuk, we prove Stone-type duality theorems for the following four categories: all of them have as objects the locally compact Hausdorff spaces, and their morphisms are, respectively, the continuous…
The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to…
Generalizing Duality Theorem of H. de Vries, we define a category which is dually equivalent to the category of all locally compact Hausdorff spaces and all perfect maps between them.
The product of a Sierpinski set and a Lusin set has Menger's property. The product of a gamma set and a Lusin set has Rothberger's property.
We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.
Contents: 2. Invited contribution: Ultrafilters and small sets 3. Research announcements 3.1. Inverse Systems and I-Favorable Spaces 3.2. Combinatorial and hybrid principles for sigma-directed families of countable sets modulo finite 3.3. A…
It is shown that every separable abelian topological group is isomorphic with a topological subgroup of a monothetic group (that is, a topological group with a single topological generator). In particular, every separable metrizable abelian…
This is a selection of open problems dealing with ``large'' (non locally compact) topological groups and concerning extreme amenability (fixed point on compacta property), oscillation stability, universal minimal flows and other aspects of…
We prove that the isometry group $\Iso(\Ur)$ of the universal Urysohn metric space $\Ur$ equipped with the natural Polish topology is a L\'evy group in the sense of Gromov and Milman, that is, admits an approximating chain of compact (in…
We show that every abelian Polish group is the topological factor-group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced…
Given a compact set $K$ in the plane, which does not contain any triple of points forming a vertical and a horizontal segment, and a map $f\in C(K)$, we give a construction of functions $g,h\in C(\mathbb R)$ such that $f(x,y)=g(x)+h(y)$ for…
We define the infinite dimensional simplex to be the closure of the convex hull of the standard basis vectors in R^infinity, and prove that this space has the 'fixed point property': any continuous function from the space into itself has a…
We prove the lemma of Knaster-Kuratowski-Mazurkiewicz as a consequence of the Lusternik-Schnirelman-Borsuk theorem.
Two classes of topological spaces are introduced on which every probability Radon measure possesses a uniformly distributed sequence or a uniformly tight uniformly distributed sequence. It is shown that these classes are stable under…
In this paper, we discuss the basic properties of Alexandroff spaces. Several examples of Alexandroff spaces are given. We show how to construct new Alexandroff spaces from given ones. Finally, two invariants for compact Alexandroff spaces…
Martin's Axiom for $\sigma$-centered partial orders implies that there is a cosmic space with non-coinciding dimensions.
The purpose of this paper is to investigate the large inductive dimension of the remainder of the Smirnov compactification of the n-dimensional Euclidean space with the usual metric, and give an application of it.
After recalling the definition of connectivity spaces and some of their main properties, a way is proposed to represent finite connectivity spaces by directed simple graphs. Then a connectivity structure is associated to each tame link. It…