Remarks on duality for -groups. I. Products and coproducts
Remarks on sequence covering images of metric spaces.
Results on controlling the residuals of perturbed Newton-like methods on Banach spaces with a convergence structure.
Right simple subsemigroups and right subgroups of compact convergence semigroups.
Rings of maps: sequential convergence and completion
The ring of all real-valued measurable functions, carrying the pointwise convergence, is a sequential ring completion of the subring of all continuous functions and, similarly, the ring of all Borel measurable subsets of is a sequential ring completion of the subring of all finite unions of half-open intervals; the two completions are not categorical. We study -rings of maps and develop a completion theory covering the two examples. In particular, the -fields of sets form an epireflective...
Selection principles and upper semicontinuous functions
In connection with a conjecture of Scheepers, Bukovský introduced properties wQN* and SSP* and asked whether wQN* implies SSP*. We prove it in this paper. We also give characterizations of properties S₁(Γ,Ω) and in terms of upper semicontinuous functions
Separation axioms for partially ordered convergence spaces.
Sequences of measurable functions
Sequential Cauchy spaces
Sequential characterizations of metrizability
Sequential completeness and -sequential completeness are different
Sequential completeness of subspaces of products of two cardinals
Let be a cardinal number with the usual order topology. We prove that all subspaces of are weakly sequentially complete and, as a corollary, all subspaces of are sequentially complete. Moreover we show that a subspace of need not be sequentially complete, but note that is sequentially complete whenever and are subspaces of .
Sequential completeness versus Čech - completeness
Sequential convergence in
I discuss the number of iterations of the elementary sequential closure operation required to achieve the full sequential closure of a set in spaces of the form .
Sequential convergences in Boolean algebras
Sequential convergences on Boolean algebras defined by systems of maximal filters
We study sequential convergences defined on a Boolean algebra by systems of maximal filters. We describe the order properties of the system of all such convergences. We introduce the category of 2-generated convergence Boolean algebras and generalize the construction of Novák sequential envelope to such algebras.
Sequential + separable vs sequentially separable and another variation on selective separability
A space X is sequentially separable if there is a countable D ⊂ X such that every point of X is the limit of a sequence of points from D. Neither “sequential + separable” nor “sequentially separable” implies the other. Some examples of this are presented and some conditions under which one of the two implies the other are discussed. A selective version of sequential separability is also considered.
Sequential structures induced by merotopies
Sequentially complete spaces
Sequentially determined convergence spaces