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In previous papers, various notions of pre-Hausdorff, Hausdorff and regular objects at a point in a topological category were introduced and compared. The main objective of this paper is to characterize each of these notions of pre-Hausdorff, Hausdorff and regular objects locally in the category of proximity spaces. Furthermore, the relationships that arise among the various , , , structures at a point are investigated. Finally, we examine the relationships between the generalized separation...
We consider properties of Tanaka spaces (introduced in Mynard F., More on strongly sequential spaces, Comment. Math. Univ. Carolin. 43 (2002), 525–530), strongly sequential spaces, and weakly sequential spaces. Applications include product theorems for these types of spaces.
Nous donnons, pour une certaine catégorie de boréliens d'un produit de deux espaces polonais, comprenant les boréliens à coupes dénombrables, une caractérisation du type "test d'Hurewicz" de ceux ne pouvant pas être rendus différence transfinie d'ouverts par changement des deux topologies polonaises.
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