Descent for compact 0-dimensional spaces.
Diagonal conditions in ordered spaces
For a space X and a regular uncountable cardinal κ ≤ |X| we say that κ ∈ D(X) if for each with |T| = κ, there is an open neighborhood W of Δ(X) such that |T - W| = κ. If then we say that X has a small diagonal, and if every regular uncountable κ ≤ |X| belongs to D(X) then we say that X has an H-diagonal. In this paper we investigate the interplay between D(X) and topological properties of X in the category of generalized ordered spaces. We obtain cardinal invariant theorems and metrization theorems...
Distributivity law for the normal triples in the category of compacta and lifting of functors to the categories of algebras
We investigate the triples in the category of compacta whose functorial parts are normal functors in the sense of E.V. Shchepin (normal triples). The problem of lifting of functors to the categories of algebras of the normal triples is considered. The distributive law for normal triples is completely described.
Dugundji spaces and topological groups
Eberlein spaces of finite metrizability number
Yakovlev [On bicompacta in -products and related spaces, Comment. Math. Univ. Carolin. 21.2 (1980), 263–283] showed that any Eberlein compactum is hereditarily -metacompact. We show that this property actually characterizes Eberlein compacta among compact spaces of finite metrizability number. Uniformly Eberlein compacta and Corson compacta of finite metrizability number can be characterized in an analogous way.
Eine Charakterisierung K-kompakter topologischer Räume.
Embedding of the ordinal segment into continuous images of Valdivia compacta
We prove in particular that a continuous image of a Valdivia compact space is Corson provided it contains no homeomorphic copy of the ordinal segment . This generalizes a result of R. Deville and G. Godefroy who proved it for Valdivia compact spaces. We give also a refinement of their result which yields a pointwise version of retractions on a Valdivia compact space.
Embeddings in contractible or compact objects
Equilateral sets in Banach spaces of the form C(K)
We show that for "most" compact nonmetrizable spaces, the unit ball of the Banach space C(K) contains an uncountable 2-equilateral set. We also give examples of compact nonmetrizable spaces K such that the minimum cardinality of a maximal equilateral set in C(K) is countable.
Espaces de mesures et compactologies
Espaces de mesures et compactologies
Espaces non verifiant le second axiome de denombrabilité.
Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions.
Extensions of compact continuous maps into decomposable sets
Fiber orders and compact spaces of uncountable weight
We study an order relation on the fibers of a continuous map and its application to the study of the structure of compact spaces of uncountable weight.
Finiteness and compactness in chain-net spaces
Folgenkompaktheit und Auswahlaxiom
Fortsetzbarkeit stetiger Abbildungen und Kompaktheitsgrad topologischer Räume.
From a Ramsey-type theorem to indepedence
Function spaces and local properties
Necessary conditions and sufficient conditions are given for to be a (σ-) m₁- or m₃-space. (A space is an m₁-space if each of its points has a closure-preserving local base.) A compact uncountable space K is given with an m₁-space, which answers questions raised by Dow, Ramírez Martínez and Tkachuk (2010) and Tkachuk (2011).