Countable small rank and cardinal invariants
Countable subsets of Suslinian continua
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 tightness in the spaces of regular probability measures
We prove that if K is a compact space and the space P(K × K) of regular probability measures on K × K has countable tightness in its weak* topology, then L₁(μ) is separable for every μ ∈ P(K). It has been known that such a result is a consequence of Martin's axiom MA(ω₁). Our theorem has several consequences; in particular, it generalizes a theorem due to Bourgain and Todorčević on measures on Rosenthal compacta.
Countable Toronto spaces
A space X is called an α-Toronto space if X is scattered of Cantor-Bendixson rank α and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprāns by constructing a countable α-Toronto space for each α ≤ ω. We also construct consistent examples of countable α-Toronto spaces for each .
Countable-dimensional spaces: a survey [Book]
Countable-points compactifications for metric spaces
Countably compact spaces all countable subsets of which are scattered
Countably determined locally convex spaces
Countably determined sets and a conjecture of C.W. Henson.
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)...
Counting shape and homotopy types among fundamental absolute neighborhood retracts: an elementary approach.
Coupled coincidence point and coupled common fixed point theorems in partially ordered metric spaces with -distance.
Coupled coincidence point theorems for nonlinear contractions in partially ordered quasi-metric spaces with a -function.
Coupled fixed point, -invariant set and fixed point of -order.