Sums of quasicontinuous functions
It is proved that every real cliquish function defined on a separable metrizable space is the sum of three quasicontinuous functions.
Super and strongly faintly continuous multifunctions.
Super real closed rings
A super real closed ring is a commutative ring equipped with the operation of all continuous functions ℝⁿ → ℝ. Examples are rings of continuous functions and super real fields attached to z-prime ideals in the sense of Dales and Woodin. We prove that super real closed rings which are fields are an elementary class of real closed fields which carry all o-minimal expansions of the real field in a natural way. The main part of the paper develops the commutative algebra of super real closed rings, by...
Support results via exceptional sets in Banach spaces
Sur deux espaces de fonctions non dérivables
Let D (resp. D*) be the subspace of C = C([0,1], R) consisting of differentiable functions (resp. of functions differentiable at the one point at least). We give topological characterizations of the pairs (C, D) and (C, D*) and use them to give some examples of spaces homeomorphic to CDor to CD*.
Sur la caractérisation topologique des compacts à l'aide des demi-treillis des pseudométriques continues
For a Tikhonov space X we denote by Pc(X) the semilattice of all continuous pseudometrics on X. It is proved that compact Hausdorff spaces X and Y are homeomorphic if and only if there is a positive-homogeneous (or an additive) semi-lattice isomorphism T:Pc(X) → Pc(Y). A topology on Pc(X) is called admissible if it is intermediate between the compact-open and pointwise topologies on Pc(X). Another result states that Tikhonov spaces X and Y are homeomorphic if and only if there exists a positive-homogeneous...
Sur la catégorie des applications quasi-continues
Sur la classificaton des continus héréditairment unicohérents
Sur la frontière d'un convexe mobile
Siano , sottoinsiemi convessi, chiusi e limitati di uno spazio normato , con le frontiere , . Dimostriamo che , dove è la metrica di Hausdorff tra sottoinsiemi chiusi di . Studiamo inoltre la continuità e la semicontinuità superiore ed inferiore di una multifunzione di tipo «frontiera».
Sur la sommabilité de familles de fonctions uniformément continues
Sur la somme et le produit combinatoire des rétractes absolus
Sur la transformation de Dirac d'un espace à génération compacte
Sur le prolongement des fonctions continues dans les complexes simpliciaux infinis
Sur le théorème de complétion de Buchwalter-Pupier
Sur les espaces annelés avec groupe d'opérateurs
Sur les fonctions cliquish
Sur les fonctions vectorielles approximativement continues
Sur les rétractes absolus Pn -valués de dimension finie
We prove that a k-dimensional hereditarily indecomposable metrisable continuum is not a -valued absolute retract. We deduce from this that none of the classical characterizations of ANR (metric) extends to the class of stratifiable spaces.
Sur les sélecteurs des multifonctions
Sur l’invariance de la dimension infinie forte par t-équivalence
Let X and Y be metric compacta such that there exists a continuous open surjection from onto . We prove that if there exists an integer k such that is strongly infinite-dimensional, then there exists an integer p such that is strongly infinite-dimensional.