Concerning Splittability and Perfect Mappings
Concerning the shapes of n-dimensional spheres
Concerning two covering properties
Connected LCA groups are sequentially connected
We prove that every connected locally compact Abelian topological group is sequentially connected, i.e., it cannot be the union of two proper disjoint sequentially closed subsets. This fact is then applied to the study of extensions of topological groups. We show, in particular, that if is a connected locally compact Abelian subgroup of a Hausdorff topological group and the quotient space is sequentially connected, then so is .
Construction functors for topological semigroups.
Continuous images and other topological properties of Valdivia compacta
We study topological properties of Valdivia compact spaces. We prove in particular that a compact Hausdorff space K is Corson provided each continuous image of K is a Valdivia compactum. This answers a question of M. Valdivia (1997). We also prove that the class of Valdivia compacta is stable with respect to arbitrary products and we give a generalization of the fact that Corson compacta are angelic.
Continuous images of which are homeomorphic to .
Contre-exemples associés aux théorèmes de Rosenthal. Quelques propriétés liées à ces résultats
Convergence in compacta and linear Lindelöfness
Let be a compact Hausdorff space with a point such that is linearly Lindelöf. Is then first countable at ? What if this is true for every in ? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is “yes” when is, in addition, -monolithic. We also prove that if is compact, Hausdorff, and is strongly discretely Lindelöf, for every in , then is first countable. An example of linearly Lindelöf...
Correction to the paper “A generalization of -compact spaces”
Correction to the paper “The Bohr compactification, modulo a metrizable subgroup” (Fund. Math. 143 (1993), 119–136)
Corrigendum to “Minimal -spaces are countably compact”
Countable Compact Scattered T₂ Spaces and Weak Forms of AC
We show that: (1) It is provable in ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) that every compact scattered T₂ topological space is zero-dimensional. (2) If every countable union of countable sets of reals is countable, then a countable compact T₂ space is scattered iff it is metrizable. (3) If the real line ℝ can be expressed as a well-ordered union of well-orderable sets, then every countable compact zero-dimensional T₂ space...
Countable compactness and -limits
For , we say that is quasi -compact, if for every there is such that , where is the Stone-Čech extension of . In this context, a space is countably compact iff is quasi -compact. If is quasi -compact and is either finite or countable discrete in , then all powers of are countably compact. Assuming , we give an example of a countable subset and a quasi -compact space whose square is not countably compact, and show that in a model of A. Blass and S. Shelah every quasi...
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.
Countably compact spaces all countable subsets of which are scattered
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)...
Descent for compact 0-dimensional spaces.