A converse to a theorem of K. Kuratowski on parametrizations of compacta on the Cantor set
A countable dense homogeneous set of reals of size ℵ₁
We prove there is a countable dense homogeneous subspace of ℝ of size ℵ₁. The proof involves an absoluteness argument using an extension of the logic obtained by adding predicates for Borel sets.
A counter-example concerning quasi-homeomorphisms of compacta
A counterexample in semimetric spaces.
A counterexample to ”Common fixed point theorem in probabilistic quasi-metric spaces".
A direct description of uniform completion in locales and a characterization of -groups
A discrete version of the Brunn-Minkowski inequality and its stability
In the first part of the paper, we define an approximated Brunn-Minkowski inequality which generalizes the classical one for metric measure spaces. Our new definition, based only on properties of the distance, allows also us to deal with discrete metric measure spaces. Then we show the stability of our new inequality under convergence of metric measure spaces. This result gives as corollary the stability of the classical Brunn-Minkowski inequality for geodesic spaces. The proof of this stability...
A factorization lemma and its application to realization of mappings as inverse limits
A factorization theorem for the transfinite kernel dimension of metrizable spaces
We prove a factorization theorem for transfinite kernel dimension in the class of metrizable spaces. Our result in conjunction with Pasynkov's technique implies the existence of a universal element in the class of metrizable spaces of given weight and transfinite kernel dimension, a result known from the work of Luxemburg and Olszewski.
A few topological problems
A fixed point approach to the stability of a functional equation of the spiral of Theodorus.
A fixed point approach to the stability of quadratic functional equation with involution.
A fixed point principle for locally expansive multifunctions
A Fixed Point Theorem for a Class of Mappings.
A fixed point theorem for multivalued maps in symmetric spaces.
A fixed point theorem for non-expansive mappings on compact metric spaces.
A formal analogy between proximity and finite dimensionality
A Galois connection between distance functions and inequality relations
Following the ideas of R. DeMarr, we establish a Galois connection between distance functions on a set and inequality relations on . Moreover, we also investigate a relationship between the functions of and .
A game and its relation to netweight and D-spaces
We introduce a two player topological game and study the relationship of the existence of winning strategies to base properties and covering properties of the underlying space. The existence of a winning strategy for one of the players is conjectured to be equivalent to the space have countable network weight. In addition, connections to the class of D-spaces and the class of hereditarily Lindelöf spaces are shown.
A general "in between theorem".