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 categorical concept of completion of objects
We introduce the concept of firm classes of morphisms as basis for the axiomatic study of completions of objects in arbitrary categories. Results on objects injective with respect to given morphism classes are included. In a finitely well-complete category, firm classes are precisely the coessential first factors of morphism factorization structures.
A Cech-Hurewicz Isomorphism Theorem for Movable Metric Compacta.
A Certain Class Of Mappings In Topological Spaces
A characterization of open mapping in terms of convergent sequences.
A characterization of point semiuniformities.
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 common end point theorem for set-valued generalized -weak contraction.
A common fixed point theorem for weakly compatible mappings.
A common fixed point theorem for weakly compatible mappings in non-Archimedean Menger PM-spaces
-compactifications and -weight of Alexandroff spaces
The paper is devoted to the study of the ordered set of all, up to equivalence, -compactifications of an Alexandroff space . The notion of -weight (denoted by ) of an Alexandroff space is introduced and investigated. Using results in ([7]) and ([5]), lattice properties of and are studied, where is the set of all, up to equivalence, -compactifications of for which . A characterization of the families of bounded functions generating an -compactification of is obtained. The notion...
A Completion for a Transitive Quasi-Uniform Space
A completion functor for Cauchy groups.
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.