Contra-continuous functions and strongly -closed spaces.
Contractive fixed points
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...
Convergence in exponentiable spaces.
Convergence of a sequence of fixed points in a uniform space
Convergence of conditional expectations for unbounded closed convex random sets
We discuss here several types of convergence of conditional expectations for unbounded closed convex random sets of the form where is a decreasing sequence of sub-σ-algebras and is a sequence of closed convex random sets in a separable Banach space.
Convergent sequences in
Coronas of ultrametric spaces
We show that, under CH, the corona of a countable ultrametric space is homeomorphic to . As a corollary, we get the same statements for the Higson’s corona of a proper ultrametric space and the space of ends of a countable locally finite group.
Correction to the paper “A generalization of -compact spaces”
Correction to the paper: Pairwise monotonically normal spaces
Correction to the paper: Sets invariant under projections onto one dimensional subspaces
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 And Uncountable Covers
Countable and Uncountable covers.
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 dense homogeneous filters and the Menger covering property
We present a ZFC construction of a non-meager filter which fails to be countable dense homogeneous. This answers a question of Hernández-Gutiérrez and Hrušák. The method of the proof also allows us to obtain for any n ∈ ω ∪ {∞} an n-dimensional metrizable Baire topological group which is strongly locally homogeneous but not countable dense homogeneous.
Countable dense homogeneous spaces