Preparacompactness and ℵ-preparacompactness in q-spaces
Products of normal spaces with Lašnev spaces
Products of perfectly normal spaces
-compact spaces and -connected spaces.
Reflective functors via nearness
Regular fuzzy spaces and fuzzy almost regular spaces
Regular spaces and relations
Regularity and normality on L-topological spaces. I.
Regularity and normality via ideals.
Relaciones entre orden, normalidad y completa regularidad.
We study some relations whose compatibility with the topology is equivalent to normality or to complete regularity.
Relative normality and product spaces
Arhangel’skiĭ defines in [Topology Appl. 70 (1996), 87–99], as one of various notions on relative topological properties, strong normality of in for a subspace of a topological space , and shows that this is equivalent to normality of , where denotes the space obtained from by making each point of isolated. In this paper we investigate for a space , its subspace and a space the normality of the product in connection with the normality of . The cases for paracompactness, more...
Relatively compact spaces and separation properties
We consider the property of relative compactness of subspaces of Hausdorff spaces. Several examples of relatively compact spaces are given. We prove that the property of being a relatively compact subspace of a Hausdorff spaces is strictly stronger than being a regular space and strictly weaker than being a Tychonoff space.
Remarks on locally closed sets.
Retracts and extension spaces for perfectly normal spaces - II
Rudin's Dowker space in the extension with a Suslin tree
We introduce a generalization of a Dowker space constructed from a Suslin tree by Mary Ellen Rudin, and the rectangle refining property for forcing notions, which modifies the one for partitions due to Paul B. Larson and Stevo Todorčević and is stronger than the countable chain condition. It is proved that Martin's Axiom for forcing notions with the rectangle refining property implies that every generalized Rudin space constructed from Aronszajn trees is non-Dowker, and that the same can be forced...
Semi separation axioms and hyperspaces.
Separating by -sets in finite powers of ω₁
It is known that all subspaces of ω₁² have the property that every pair of disjoint closed sets can be separated by disjoint -sets (see [4]). It has been conjectured that all subspaces of ω₁ⁿ also have this property for each n < ω. We exhibit a subspace of ⟨α,β,γ⟩ ∈ ω₁³: α ≤ β ≤ γ which does not have this property, thus disproving the conjecture. On the other hand, we prove that all subspaces of ⟨α,β,γ⟩ ∈ ω₁³: α < β < γ have this property.
Separation axioms as absolute properties under monotone unions in weak topology
Separation axioms, covering properties, and inverse limits generated by developable topological spaces [Book]
Separation axioms for partially ordered convergence spaces.