We continue from “part I” our address of the following situation. For a Tychonoff space Y, the “second epi-topology” σ is a certain topology on C(Y), which has arisen from the theory of categorical epimorphisms in a category of lattice-ordered groups. The topology σ is always Hausdorff, and σ interacts with the point-wise addition + on C(Y) as: inversion is a homeomorphism and + is separately c...

Topological groups whose underlying spaces are basically disconnected, F-, or F′-spaces but not P-spaces considered. It is proved, in particular, that the existence of a Lindelöf disconnected topological group which P-space equivalent to Boolean countable pseudocharacter, free and Abelian zero-dimensional non-P-spaces never F′-spaces, F′-group selective ultrafilters on ω.

We will introduce and study the pairwise weakly regular-Lindelöf bitopological spaces and obtain some results. Furthermore, we study the pairwise weakly regular-Lindelöf subspaces and subsets, and investigate some of their characterizations. We also show that a pairwise weakly regularLindelöf property is not a hereditary property. Some counterexamples will be considered in order to establish so...

A space X is a D-space if whenever one is given a neighborhood N(x) of x for each x ∈ X, then there is a closed discrete subset D of X such that {N(x) : x ∈ D} covers X. It is a decades-old open question whether some of the standard covering properties, such as Lindelöf or paracompact, imply D . This remains unsettled, yet there has been a considerable amount of interesting recent work on D-spa...

We continue the study of a lattice-ordered ring G(X), associated with the ring C(X). Following [10], X called RG when G(X) = C(Xδ). An RG-space must have a dense set of very weak P-points. It must have a dense set of almost-P-points if Xδ is Lindelöf, or if the continuum hypothesis holds and C(X) has small cardinality. Space which are RG must have finite Krull dimension when taken with respect ...

For each space, Ufin(Γ,Ω) is equivalent to Sfin(Ω,O) and this selection property has game-theoretic and Ramsey-theoretic characterizations (Theorem 2). For Lindelöf space X we characterize when a subspace Y is relatively Hurewicz in X in terms of selection principles (Theorem 9), and for metrizable X in terms of basis properties, and measurelike properties (Theorems 14 and 16). Using the Contin...

We prove that if X is a regular space with no uncountable free sequences, then the tightness of its $$G_\delta $$ topology at most continuum and is, in addition, assumed to be Lindelöf contains sequences length larger continuum. also show that, surprisingly, higher cardinal generalization our theorem does not hold, by constructing than $$\omega _1$$ , but whose can have arbitrarily large tightn...

in this paper we formulate and prove some xed and common xed pointtheorems for self-mappings dened on complete lower transversal functionalprobabilistic spaces.

We deal with a conjectured dichotomy for compact Hausdorff spaces: each such space contains a non-trivial converging ω-sequence or a non-trivial converging ω1-sequence. We establish that this dichotomy holds in a variety of models; these include the Cohen models, the random real models and any model obtained from a model of CH by an iteration of property K posets. In fact in these models every ...