THIN-VERY TALL COMPACT SCATTERED SPACES WHICH ARE HEREDITARILY SEPARABLE

Autor(es)

Brech, Christina ^[1] ; Koszmider, Piotr ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Inst Math Stat & Sci Comp, BR-13083970 Campinas, SP - Brazil

^[2] Tech Univ Lodz, Inst Matemat, PL-90924 Lodz - Poland

• Tipo de documento: Artigo Científico
• Fonte: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 363, n. 1, p. 501-519, JAN 2011.
• Citações Web of Science: 5

Resumo

We strengthen the property Delta of a function f : {[}omega(2)](2) -> {[}omega(2)](<=omega) considered by Baumgartner and Shelah. This allows us to consider new types of amalgamations in the forcing used by Rabus, Juhasz and Soukup to construct thin-very tall compact scattered spaces. We consistently obtain spaces K as above where K(n) is hereditarily separable for each n is an element of N. This serves as a counterexample concerning cardinal functions on compact spaces as well as having some applications in Banach spaces: the Banach space C(K) is an Asplund space of density N(2) which has no Frechet smooth reforming, nor an uncountable biorthogonal system. (AU)

• Processo FAPESP: 06/02378-7 - Análise em dimensão infinita
• Beneficiário: Jorge Tulio Mujica Ascui
• Modalidade de apoio: Auxílio à Pesquisa - Temático