On some notions related to compactness for locales
On the closure of the bicyclic semigroup.
On the extent of separable, locally compact, selectively (a)-spaces
The author has recently shown (2014) that separable, selectively (a)-spaces cannot include closed discrete subsets of size . It follows that, assuming CH, separable selectively (a)-spaces necessarily have countable extent. However, in the same paper it is shown that the weaker hypothesis "" is not enough to ensure the countability of all closed discrete subsets of such spaces. In this paper we show that if one adds the hypothesis of local compactness, a specific effective (i.e., Borel) parametrized...
On the level spaces of fuzzy topological spaces.
On the subsets of non locally compact points of ultracomplete spaces
In 1998, S. Romaguera [13] introduced the notion of cofinally Čech-complete spaces equivalent to spaces which we later called ultracomplete spaces. We define the subset of points of a space at which is not locally compact and call it an nlc set. In 1999, Garc’ıa-Máynez and S. Romaguera [6] proved that every cofinally Čech-complete space has a bounded nlc set. In 2001, D. Buhagiar [1] proved that every ultracomplete GO-space has a compact nlc set. In this paper, ultracomplete spaces which have...
On topologies generating the Effros Borel structure and on the Effros measurability of the boundary operation
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 universality of finite powers of locally path-connected meager spaces
It is shown that for every integer n the (2n+1)th power of any locally path-connected metrizable space of the first Baire category is 𝓐₁[n]-universal, i.e., contains a closed topological copy of each at most n-dimensional metrizable σ-compact space. Also a one-dimensional σ-compact absolute retract X is found such that the power X^{n+1} is 𝓐₁[n]-universal for every n.
On -regular spaces.
Operator compactification of topological spaces.
Perfectly supportable semigroups are σ-discrete in each Hausdorff shift-invariant topology
In this paper we introduce perfectly supportable semigroups and prove that they are σ-discrete in each Hausdorff shiftinvariant topology. The class of perfectly supportable semigroups includes each semigroup S such that FSym(X) ⊂ S ⊂ FRel(X) where FRel(X) is the semigroup of finitely supported relations on an infinite set X and FSym(X) is the group of finitely supported permutations of X.
Products of topological spaces represent any semigroup (Preliminary communication)
Properties of a pair of functions which generate a dense subsemigroup of S(X).
Pro-reflections and pro-factorizations
Recurrent functions and semigroups.
Regular and Other Kinds of Extensions of Topological Spaces
∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.In this paper the notion of SR-proximity is introduced and in virtue of it some new proximity-type descriptions of the ordered sets of all (up to equivalence) regular, resp. completely regular, resp. locally compact extensions of a topological space are obtained. New proofs of the Smirnov Compactification Theorem [31] and of the...
Regulated semilattices and locally compact spaces
Relative compactness and recent common generalizations of metric and locally compact spaces
Relatively realcompact sets and nearly pseudocompact spaces
A space is said to be nearly pseudocompact iff is dense in . In this paper relatively realcompact sets are defined, and it is shown that a space is nearly pseudocompact iff every relatively realcompact open set is relatively compact. Other equivalences of nearly pseudocompactness are obtained and compared to some results of Blair and van Douwen.
Representation Theorem for Minimal -Algebras