-spaces and images of separable metric spaces.
-approximable compact spaces
For every topological property , we define the class of -approximable spaces which consists of spaces X having a countable closed cover such that the “section” has the property for each . It is shown that every -approximable compact space has , if is one of the following properties: countable tightness, -scatteredness with respect to character, -closedness, sequentiality (the last holds under MA or ). Metrizable-approximable spaces are studied: every compact space in this class has...
-dimension function of bitopological spaces
-closed sets in biclosure spaces
In the present paper, we introduce and study the concept of -closed sets in biclosure spaces and investigate its behavior. We also introduce and study the concept of -continuous maps.
-fuzzy nonlinear approximation theory with application.
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.