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Una variedad diferenciable de dimensión infinita, separada y no regular.

Juan Margalef Roig, Enrique Outerelo Domínguez (1982)

Revista Matemática Hispanoamericana

A partir de un espacio de Hilbert, E, de dimensión infinita separable y de un elemento λ de L(E,R) - {0} se construye un homeomorfismo h0 de(Eλ+ - Ker λ) U {0}sobre E con las topologías usuales tal que h0(0) = 0 y h0|Eλ+ - Ker λ es un difeomorfismo de clase ∞ de Eλ+ - Ker λ sobre E - {0}, con las estructuras diferenciables de clase ∞ usuales. Mediante h0 se construye una variedad diferenciable de dimensión infinita, separada y no regular.

Une extension d'un théorème de fonctions implicites de Hamilton

Francis Sergeraert (1976)

Mémoires de la Société Mathématique de France

Vers une notion de dérivation fonctionnelle causale

Michel Fliess (1986)

Annales de l'I.H.P. Analyse non linéaire

Weak* sequential compactness and bornological limit derivatives.

Borwein, Jonathan, Fitzpatrick, Simon (1995)

Journal of Convex Analysis

$σ$ -porosity is separably determined

Marek Cúth, Martin Rmoutil (2013)

Czechoslovak Mathematical Journal

We prove a separable reduction theorem for $σ$ -porosity of Suslin sets. In particular, if $A$ is a Suslin subset in a Banach space $X$ , then each separable subspace of $X$ can be enlarged to a separable subspace $V$ such that $A$ is $σ$ -porous in $X$ if and only if $A \cap V$ is $σ$ -porous in $V$ . Such a result is proved for several types of $σ$ -porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem...