A boundary set for the Hilbert cube containing no arcs
A -continuum is metrizable if and only if it admits a Whitney map for .
A Cantor set in the plane that is not σ-monotone
A metric space (X,d) is monotone if there is a linear order < on X and a constant c such that d(x,y) ≤ cd(x,z) for all x < y < z in X, and σ-monotone if it is a countable union of monotone subspaces. A planar set homeomorphic to the Cantor set that is not σ-monotone is constructed and investigated. It follows that there is a metric on a Cantor set that is not σ-monotone. This answers a question raised by the second author.
A combinatorial proof of the extension property for partial isometries
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
A Cone of Inhomogeneous Second-Order Polynomials.
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 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 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 theorem for multivalued maps in symmetric spaces.
A fixed point theorem for non-expansive mappings on compact metric spaces.
A general invariant metrization theorem for compact spaces
A Maximality Principle On Ordered Metric Spaces.
A metric tangential calculus.
A metrization theorem
A metrization theorem for countably compact spaces
A metrization theorem for developable spaces
A new look at pointfree metrization theorems
We present a unified treatment of pointfree metrization theorems based on an analysis of special properties of bases. It essentially covers all the facts concerning metrization from Engelking [1] which make pointfree sense. With one exception, where the generalization is shown to be false, all the theorems extend to the general pointfree context.