Convergence of convex functions and generalized inf-convolutive approximations. (Convergences des fonctions convexes et approximations inf-convolutives généralisées.)
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...
We characterize the countable compactness of lexicographic products of GO-spaces. Applying this characterization about lexicographic products, we see:
We prove by using well-founded trees that a countable product of supercomplete spaces, scattered with respect to Čech-complete subsets, is supercomplete. This result extends results given in [Alstera], [Friedlera], [Frolika], [HohtiPelantb], [Pelanta] and its proof improves that given in [HohtiPelantb].
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.