On weak Normality and Selectivity of Ultrafilters
On weaker forms of compactness, Lindelöfness, and countable compactness.
On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces
We introduce the concept of a family of sets generating another family. Then we prove that if X is a topological space and X has W = {W(x): x ∈ X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of ω-rank, then X is metaLindelöf as well as a countable product of them. We also prove that if W satisfies ω-rank (F) and, for every x ∈ X, W(x) is of the form W 0(x) ∪ W 1(x), where W 0(x) is Noetherian and W 1(x) consists of neighbourhoods of...
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 weakly closed functions
On Weakly Measurable Functions
We show that if T is an uncountable Polish space, 𝓧 is a metrizable space and f:T→ 𝓧 is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f[T∖M] is a separable space. We also give an example showing that "metrizable" cannot be replaced by "normal".
On weakly monotonically monolithic spaces
In this note, we introduce the concept of weakly monotonically monolithic spaces, and show that every weakly monotonically monolithic space is a -space. Thus most known conclusions on -spaces can be obtained by this conclusion. As a corollary, we have that if a regular space is sequential and has a point-countable -network then is a -space.
On weak-open -images of metric spaces
In this paper, we give some characterizations of metric spaces under weak-open -mappings, which prove that a space is -developable (or Cauchy) if and only if it is a weak-open -image of a metric space.
On (X, p)- spaces
On -normal and -normal spaces
We define two natural normality type properties, -normality and -normality, and compare these notions to normality. A natural weakening of Jones Lemma immediately leads to generalizations of some important results on normal spaces. We observe that every -normal, pseudocompact space is countably compact, and show that if is a dense subspace of a product of metrizable spaces, then is normal if and only if is -normal. All hereditarily separable spaces are -normal. A space is normal if and...
On --open sets and a decomposition of almost--continuity.
On -continuous selections of small multifunctions and covering properties
The spaces for which each -continuous function can be extended to a -small point-open l.s.cṁultifunction (resp. point-closed u.s.cṁultifunction) are studied. Some sufficient conditions and counterexamples are given.
On -sets and associated weak separation axioms.
On --open sets.
On -closed sets and some forms of continuity
In this paper, we further the study of -compactness a generalization of quasi-H-closed sets and its applications to some forms of continuity using -open and -open sets. Among other results, it is shown a weakly -retract of a Hausdorff space is a -closed subset of .
On -continuity and strong -continuity.
On -generalized closed sets.
On -regular spaces.
On κ-Lindelöf spaces
We use the Hausdorff pseudocharacter to bound the cardinality and the Lindelöf degree of κ-Lindelöf Hausdorff spaces.
On -images of separable metric spaces and a problem of Shou Lin