On transfinite inductive compactness degree
On treelike proximity spaces
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 two classes of paracompact spaces
On Typical Compact Convex Sets in Hilbert Spaces
Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.
On U-equivalence spaces
In this paper induced U-equivalence spaces are introduced and discussed. Also the notion of U- equivalently open subsets of a U-equivalence space and U-equivalently open functions are studied. Finally, equivalently uniformisable topological spaces are considered.
On ultrametric space.
On uncountable unions and intersections of measurable sets.
On uniform connectedness.
On uniform connection properties
On uniform paracompactness
On uniform paracompactness of the -metric spaces
Gli spazi -metrici uniformemente numerabilmente paracompatti sono uniformemente paracompatti. Si fornisce altresì una caratterizzazione degli spazi -metrici fini.
On uniform spaces
On Uniform Spaces where All Uniformly Continuous Functions are Bounded.
On uniform spaces with linearly ordered bases II (-metric spaces)
On uniformly locally compact quasi-uniform hyperspaces
We characterize those Tychonoff quasi-uniform spaces for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family of nonempty compact subsets of . We deduce, among other results, that the Hausdorff-Bourbaki quasi-uniformity of the locally finite quasi-uniformity of a Tychonoff space is uniformly locally compact on if and only if is paracompact and locally compact. We also introduce the notion of a co-uniformly locally compact quasi-uniform space and show...
On uniformly regular measures
On unitary Cauchy filters on topological monoids
For Hausdorff topological monoids, the concept of a unitary Cauchy net is a generalization of the concept of a fundamental sequence of reals. We consider properties and applications of such nets and of corresponding filters and prove, in particular, that the underlying set of a given monoid, endowed with the family of such filters, forms a Cauchy space whose convergence structure defines a uniform topology. A commutative monoid endowed with the corresponding uniformity is uniform. A distant purpose...
On unitary extensions and unitary completions of topological monoids
The concept of a unitary Cauchy net in an arbitrary Hausdorff topological monoid generalizes the concept of a fundamental sequence of reals. We construct extensions of this monoid where all its unitary Cauchy nets converge.
On universal infinite-dimensional spaces