Correction to the paper “The Bohr compactification, modulo a metrizable subgroup” (Fund. Math. 143 (1993), 119–136)
Corrections : «Les dérivations analytiques»
Corrections to my paper "Investigating the ANR-property of metric spaces" (Fund. Math. 124 (1984), 243-254)
Corrections to: “Remarks on subsets of Cartesian products of metric spaces”
Corrections to the paper “The cartesian closed topological hull of the category of completely regular filterspaces”
Correspondence between interval -equivalences and -functions
Corrigendum: On semi-homeomorphisms.
Corrigendum to “Minimal -spaces are countably compact”
Corrigendum to "On density modulo 1 of some expressions containing algebraic integers" (Acta Arith. 127 (2007), 217-229)
Corrigendum to "Products of pseudoradial spaces".
Corrigendum to the paper "Semigroup actions on tori and stationary measures on projective spaces" (Studia Math. 171 (2005), 33-66)
Coshape-invariant functors and Mackey's induced representation theorem
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 compactness of lexicographic products of GO-spaces
We characterize the countable compactness of lexicographic products of GO-spaces. Applying this characterization about lexicographic products, we see:
Countable decomposition of derivatives and Baire 1 functions.
Countable dense homogeneity and n-homogeneity
Countable dense homogeneity and λ-sets
We show that all sufficiently nice λ-sets are countable dense homogeneous (𝖢𝖣𝖧). From this fact we conclude that for every uncountable cardinal κ ≤ 𝔟 there is a countable dense homogeneous metric space of size κ. Moreover, the existence of a meager in itself countable dense homogeneous metric space of size κ is equivalent to the existence of a λ-set of size κ. On the other hand, it is consistent with the continuum arbitrarily large that every 𝖢𝖣𝖧 metric space has size either ω₁ or 𝔠. An...