On the l-equivalence of metric spaces
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 quantification of uniform properties
Approach spaces ([4], [5]) turned out to be a natural setting for the quantification of topological properties. Thus a measure of compactness for approach spaces generalizing the well-known Kuratowski measure of non-compactness for metric spaces was defined ([3]). This article shows that approach uniformities (introduced in [6]) have the same advantage with respect to uniform concepts: they allow a nice quantification of uniform properties, such as total boundedness and completeness.
On the relationships among the axioms for a metric space and for general axiomatic systems
On the shape of MAR and MANR-spaces
On the surjective span and semispan of connected metric spaces
On the tangency of sets in generalized metric spaces for certain functions of the class
On the tangency of sets in metric spaces
On the weak-open images of metric spaces
In this paper, we give characterizations of certain weak-open images of metric spaces.
On the weight of nowhere dense subsets in compact spaces.
On the -primitive
On three equivalences concerning Ponomarev-systems
Let be a sequence of covers of a space such that is a network at in for each . For each , let and be endowed the discrete topology. Put forms a network at some point and by choosing for each . In this paper, we prove that is a sequentially-quotient (resp. sequence-covering, compact-covering) mapping if and only if each is a -cover (resp. -cover, -cover) of . As a consequence of this result, we prove that is a sequentially-quotient, -mapping if and only if it is...
On topologies generating the Effros Borel structure and on the Effros measurability of the boundary operation
On trivially semi-metrizable and D-completely regular mappings
Trivially symmetrizable, trivially semi-metrizable and trivially D-completely regular mappings are defined. They are characterized as mappings parallel to symmetrizable, semi-metrizable and D-completely regular spaces correspondently. One shows that trivially D-completely regular mappings, i.e. submappings of fibrewise products of developable mappings coincide (up to homeomorphisms) with submappings of fibrewise products of semi-metrizable mappings.
On ultrametric space.
On uniform spaces with linearly ordered bases II (-metric spaces)
On Urysohn's universal separable metric space
On Weakly Measurable Functions
We show that if T is an uncountable Polish space, 𝓧 is a metrizable space and f:T→ 𝓧 is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f[T∖M] is a separable space. We also give an example showing that "metrizable" cannot be replaced by "normal".
On weak-open compact images of metric spaces.