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.
On -distance in three dimensional space.
On -images of metric spaces.
On -metrizable spaces, their continuous images and products
A space is said to be -metrizable if it has a -discrete -base. The behavior of -metrizable spaces under certain types of mappings is studied. In particular we characterize strongly -separable spaces as those which are the image of a -metrizable space under a perfect mapping. Each Tychonoff space can be represented as the image of a -metrizable space under an open continuous mapping. A question posed by Arhangel’skii regarding if a -metrizable topological group must be metrizable receives...
On --images of metric spaces.
On -discrete Borel mappings via quasi-metrics
On -discreteness in uniform spaces
Only 3-generalized metric spaces have a compatible symmetric topology
We prove that every 3-generalized metric space is metrizable. We also show that for any ʋ with ʋ ≥ 4, not every ʋ-generalized metric space has a compatible symmetric topology.