Semi-topological properties.
Separable extensions of first countable spaces
Separation axioms for partially ordered convergence spaces.
Sequences of measurable functions
Sequential Cauchy spaces
Sequential characterizations of metrizability
Sequential compactness vs. countable compactness
The general question of when a countably compact topological space is sequentially compact, or has a nontrivial convergent sequence, is studied from the viewpoint of basic cardinal invariants and small uncountable cardinals. It is shown that the small uncountable cardinal 𝔥 is both the least cardinality and the least net weight of a countably compact space that is not sequentially compact, and that it is also the least hereditary Lindelöf degree in most published models. Similar results, some definitive,...
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 space methods in general topological spaces
Sequential structures induced by merotopies
Sequentially complete spaces
Sequentially continuous mappings of product spaces
Sequentially determined convergence spaces
Seven characterizations of non-meager 𝖯-filters
We give several topological/combinatorial conditions that, for a filter on ω, are equivalent to being a non-meager -filter. In particular, we show that a filter is countable dense homogeneous if and only if it is a non-meager -filter. Here, we identify a filter with a subspace of through characteristic functions. Along the way, we generalize to non-meager -filters a result of Miller (1984) about -points, and we employ and give a new proof of results of Marciszewski (1998). We also employ a theorem...