On strong convergence of multivalued maps
On strong form of Arzela convergence.
On summability in convergence -groups
On surjective kernels of partial algebras.
On the convergence and character spectra of compact spaces
An infinite set A in a space X converges to a point p (denoted by A → p) if for every neighbourhood U of p we have |A∖U| < |A|. We call cS(p,X) = |A|: A ⊂ X and A → p the convergence spectrum of p in X and cS(X) = ⋃cS(x,X): x ∈ X the convergence spectrum of X. The character spectrum of a point p ∈ X is χS(p,X) = χ(p,Y): p is non-isolated in Y ⊂ X, and χS(X) = ⋃χS(x,X): x ∈ X is the character spectrum of X. If κ ∈ χS(p,X) for a compactum X then κ,cf(κ) ⊂ cS(p,X). A selection of our results (X...
On the convergence of certain sequences and some applications
On the existence of true uniform ultrafilters
We shall show that there is an ultrafilter on singular with countable cofinality, which cannot be reached from the set of all subuniform ultrafilters by iterating the closure of sets of size .
On the extensibility of closed filters in T spaces and the existence of well orderable filter bases
We show that the statement CCFC = “the character of a maximal free filter of closed sets in a space is not countable” is equivalent to the Countable Multiple Choice Axiom CMC and, the axiom of choice AC is equivalent to the statement CFE = “closed filters in a space extend to maximal closed filters”. We also show that AC is equivalent to each of the assertions: “every closed filter in a space extends to a maximal closed filter with a well orderable filter base”, “for every set ,...
On the limits of sequences of Darboux a.e. quasi-continuous functions
On the Novák completion of convergence groups
On the quasi-uniform convergence of transfinite sequences of functions.
On the sequential order
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 the tightness of chain-net spaces
On topologies generating the Effros Borel structure and on the Effros measurability of the boundary operation
On totally non-commutative convergence groupoids
On transfinite convergence and generalized continuity
On weakly bisequential spaces
Weakly bisequential spaces were introduced by A.V. Arhangel'skii [1], in this paper. We discuss the relations between weakly bisequential spaces and metric spaces, countably bisequential spaces, Fréchet-Urysohn spaces.
On -regular spaces.
One-point compactification on convergence spaces.