On the extension of continuous functions
On the extensions of uniformly continuous mappings
On the fundamental dimension of the Cartesian product of compacta with the fundamental dimension 2
On the fundamental group of the fixed points of an unipotent action.
On the generalizations of Siegel's fixed point theorem.
In this paper, we establish a new version of Siegel's fixed point theorem in generating spaces of quasi-metric family. As consequences, we obtain general versions of the Downing-Kirk's fixed point and Caristi's fixed point theorem in the same spaces. Some applications of these results to fuzzy metric spaces and probabilistic metric spaces are presented.
On the generalized property
On the gluing of hyperconvex metrics and diversities
In this work we consider two hyperconvex diversities (or hyperconvex metric spaces) (X, δX) and (Y, δY ) with nonempty intersection and we wonder whether there is a natural way to glue them so that the new glued diversity (or metric space) remains being hyperconvex. We provide positive and negative answers in both situations.
On the group of isometries of the Urysohn universal metric space
On the group of isometries on a locally compact metric space.
On the inverse image of Baire spaces.
On the iterative test for j-contractive mappings in uniform spaces
Edelstein iterative test for j-contractive mappings in uniform spaces is established.
On the -Baire property
In this note we show the following theorem: “Let be an almost -discrete space, where is a regular cardinal. Then is -Baire iff it is a -Baire space and every point- open cover of such that is locally- at a dense set of points.” For we obtain a well-known characterization of Baire spaces. The case is also discussed.
On the l-equivalence of metric spaces
On the locally fine construction in uniform spaces, locales and formal spaces
On the lower hull of convex functions.
On the metric reflection of a pseudometric space in ZF
We show: (i) The countable axiom of choice is equivalent to each one of the statements: (a) a pseudometric space is sequentially compact iff its metric reflection is sequentially compact, (b) a pseudometric space is complete iff its metric reflection is complete. (ii) The countable multiple choice axiom is equivalent to the statement: (a) a pseudometric space is Weierstrass-compact iff its metric reflection is Weierstrass-compact. (iii) The axiom of choice is equivalent to each one of the...
On the metrizability of -spaces and its relationship to the normal Moore space conjecture
On the non-separable descriptive theory
On the preservation of Baire and weakly Baire category
We consider the question of preservation of Baire and weakly Baire category under images and preimages of certain kind of functions. It is known that Baire category is preserved under image of quasi-continuous feebly open surjections. In order to extend this result, we introduce a strictly larger class of quasi-continuous functions, i.e. the class of quasi-interior continuous functions. We show that Baire and weakly Baire categories are preserved under image of feebly open quasi-interior continuous...
On the property p and separation axioms for bitopological spaces