Countable locally connected Urysohn spaces
Countable paracompactness of inverse limits and products
Countable products of spaces of finite sets
We consider the compact spaces σₙ(Γ) of subsets of Γ of cardinality at most n and their countable products. We give a complete classification of their Banach spaces of continuous functions and a partial topological classification.
Countable sums and products of Loeb and selective metric spaces
We investigate the role that weak forms of the axiom of choice play in countable Tychonoff products, as well as countable disjoint unions, of Loeb and selective metric spaces.
Countable-points compactifications for metric spaces
Countably compact spaces all countable subsets of which are scattered
Countably evaluating homomorphisms on real function algebras
By studying algebra homomorphisms, which act as point evaluations on each countable subset, we obtain improved results on the question when all algebra homomorphisms are point evaluations.
Countably -compact spaces.
Countably metacompact spaces in the constructible universe
We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a . In addition some nonperfect spaces with σ-disjoint bases are constructed.
Countably -closed spaces
Countably z-compact spaces
In this work we study countably z-compact spaces and z-Lindelof spaces. Several new properties of them are given. It is proved that every countably z-compact space is pseuodocompact (a space on which every real valued continuous function is bounded). Spaces which are countably z-compact but not countably compact are given. It is proved that a space is countably z-compact iff every countable z-closed set is compact. Characterizations of countably z-compact and z-Lindelof spaces by multifunctions...
Counting linearly ordered spaces
For a transfinite cardinal κ and i ∈ 0,1,2 let be the class of all linearly ordered spaces X of size κ such that X is totally disconnected when i = 0, the topology of X is generated by a dense linear ordering of X when i = 1, and X is compact when i = 2. Thus every space in ℒ₁(κ) ∩ ℒ₂(κ) is connected and hence ℒ₁(κ) ∩ ℒ₂(κ) = ∅ if , and ℒ₀(κ) ∩ ℒ₁(κ) ∩ ℒ₂(κ) = ∅ for arbitrary κ. All spaces in ℒ₁(ℵ₀) are homeomorphic, while ℒ₂(ℵ₀) contains precisely ℵ₁ spaces up to homeomorphism. The class ℒ₁(κ)...
Courbe des trisecantes a une courbe lisse de P3 de degre d > 2g + 1.
Covering dimension modulo a class of spaces
Covering properties in countable products, II
In this paper, we discuss covering properties in countable products of Čech-scattered spaces and prove the following: (1) If is a perfect subparacompact space and is a countable collection of subparacompact Čech-scattered spaces, then the product is subparacompact and (2) If is a countable collection of metacompact Čech-scattered spaces, then the product is metacompact.
Covering Properties of Continua and Mappings
Coverings by closed sets
Cp-movable at infinity spaces, compact ANR divisors and property UVWn.
Criterion of Normality of the Completely Regular Topology of Separate Continuity
2000 Mathematics Subject Classification: 54C10, 54D15, 54G12.For given completely regular topological spaces X and Y, there is a completely regular space X ~⊗ Y such that for any completely regular space Z a mapping f : X × Y ⊗ Z is separately continuous if and only if f : X ~⊗ Y→ Z is continuous. We prove a necessary condition of normality, a sufficient condition of collectionwise normality, and a criterion of normality of the products X ~⊗ Y in the case when at least one factor is scattered.
Criterios De Convergencia Secuencial.