Representations of commutative semigroups by products of metric -dimensional spaces
Representations of presheaves of semiuniformisable spaces, and representation of a presheaf by the presheaf of all continuous sections in its covering-space
Residuality of the set of embeddings into Nagata's n-dimensional universal spaces
Residually finite congruences and quasi-regular subsets in uniform algebras
Resolving a question of Arkhangel'skiĭ's
We construct in ZFC a cosmic space that, despite being the union of countably many metrizable subspaces, has covering dimension equal to 1 and inductive dimensions equal to 2.
Results and problems concerning compactifications, compact subtopologies, and mappings
Rétractions dans les espaces stratifiables
Rosenthal compacta and NIP formulas
We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about ϕ-types for ϕ NIP. In particular, we show that if M is a countable model, then an M-invariant ϕ-type is Borel-definable. Also, the space of M-invariant ϕ-types is a Rosenthal compactum, which implies a number of topological tameness properties.
-metrizable spaces and related matters.
Samuel compactification and uniform coreflection of nearness -frames
We introduce the structure of a nearness on a -frame and construct the coreflection of the category of nearness -frames to the category of compact regular -frames. This description of the Samuel compactification of a nearness -frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform -frames in [11]. We also construct the uniform coreflection of a nearness -frame, that is, the coreflection of the category of to the category...
Schälbare Cohen-Macauley-Komplexe und ihre Parametrisierung.
Selection principles and Baire spaces
Selection theorems for partitions of Polish spaces
Selections that characterize topological completeness
We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].
Selections using orderings (non-separable case)
Semi -continuity in intuitionistic fuzzy topological spaces.
Semi-confluent mappings.
Semicontinuity of maps which are limits of sequences of quasi-continuous maltivalued maps
Semi-contractions des espaces localement compacts et cas des variétés complexes
En nous inspirant d’articles de Beardon, nous donnons des résultats concernant les points fixes et les orbites d’auto-applications contractantes et semi-contractantes des espaces connexes localement compacts. Des résultats plus précis sont obtenus dans le cas des variétés complexes Kobayashi hyperboliques.
Semiconvex compacta
We define and investigate a generalization of the notion of convex compacta. Namely, for semiconvex combination in a semiconvex compactum we allow the existence of non-trivial loops connecting a point with itself. It is proved that any semiconvex compactum contains two non-empty convex compacta, the center and the weak center. The center is the largest compactum such that semiconvex combination induces a convex structure on it. The convex structure on the weak center does not necessarily coincide...