| Autor(es): |
Bru, Jean-Bernard
;
de Siqueira Pedra, Walter
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | JOURNAL OF CONVEX ANALYSIS; v. 29, n. 1, p. 48-pg., 2022-01-01. |
| Resumo | |
We propose a new class of hypertopologies, called here weak* hypertopologies, on the dual space X* of a real or complex topological vector space X. The most well-studied and well-known hypertopology is the one associated with the Hausdorff metric for closed sets in a complete metric space. Therefore, we study in detail its corresponding weak* hypertopology, constructed from the Hausdorff distance on the field (i.e. R or C) of the vector space X and named here the weak*-Hausdorff hypertopology. It has not been considered so far and we show that it can have very interesting mathematical connections with other mathematical fields, in particular with mathematical logics. We explicitly demonstrate that weak* hypertopologies are very useful and natural structures by using again the weak*-Hausdorff hypertopology in order to study generic convex weak*-compact sets in great generality. We show that convex weak*-compact sets have generically a weak*-dense set of extreme points in infinite dimensions. An extension of the well-known Straszewicz theorem to Gateaux-differentiability (non necessarily Banach) spaces is also proven in the scope of this application. (AU) | |
| Processo FAPESP: | 17/22340-9 - Métodos construtivos para férmions interagentes com aplicações a teoria microscópica da condutividade e supercondutividade |
| Beneficiário: | Walter Alberto de Siqueira Pedra |
| Modalidade de apoio: | Auxílio à Pesquisa - Pesquisador Visitante - Internacional |