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
On -metrizable spaces, their continuous images and products
A space is said to be -metrizable if it has a -discrete -base. The behavior of -metrizable spaces under certain types of mappings is studied. In particular we characterize strongly -separable spaces as those which are the image of a -metrizable space under a perfect mapping. Each Tychonoff space can be represented as the image of a -metrizable space under an open continuous mapping. A question posed by Arhangel’skii regarding if a -metrizable topological group must be metrizable receives...
On σ-connected spaces
On σ-discrete coverings consisting of connected sets
On Σ-products of Σ-spaces