A Cone of Inhomogeneous Second-Order Polynomials.
A continuous dependence of fixed points of -contractive mappings in uniform spaces
The main purpose of the present paper is to established conditions for a continuous dependence of fixed points of -contractive mappings in uniform spaces. An application to nonlinear functional differential equations of neutral type have been made.
A continuous operator extending fuzzy ultrametrics
We consider the problem of simultaneous extension of fuzzy ultrametrics defined on closed subsets of a complete fuzzy ultrametric space. We construct an extension operator that preserves the operation of pointwise minimum of fuzzy ultrametrics with common domain and an operation which is an analogue of multiplication by a constant defined for fuzzy ultrametrics. We prove that the restriction of the extension operator onto the set of continuous, partial fuzzy ultrametrics is continuous with respect...
A continuous operator extending ultrametrics
The problem of continuous simultaneous extension of all continuous partial ultrametrics defined on closed subsets of a compact zero-dimensional metric space was recently solved by E.D. Tymchatyn and M. Zarichnyi and improvements to their result were made by I. Stasyuk. In the current paper we extend these results to complete, bounded, zero-dimensional metric spaces and to both continuous and uniformly continuous partial ultrametrics.
A contraction theorem in Menger probabilistic metric spaces.
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.