Construções genéricas de espaços de Asplund C(K) / Generic constructions of Asplund spaces C(K)
AUTOR(ES)
Christina Brech
DATA DE PUBLICAÇÃO
2008
RESUMO
In this work we consider a method of generic constructions of compact scattered non-metrizable spaces developed by Baumgartner, Shelah, Rabus, Juhasz and Soukup. We introduce new techniques and obtain new applications both relevant to topology of compact spaces and the geometry of Banach spaces of continuous functions. The new techniques concern new amalgamations of conditions of forcing which add the dispersed spaces as well as the generalizations of arguments of the above-mentioned authors from points of a compact space K to Radon measures on K. As applications we obtain two compact scattered spaces K_1 and K_2 with the properties below. K_1 is a hereditarily separable space of weight aleph_1 such that C(K_1) has property (C) of Corson and does not have property (E) of Efremov. K_2 is the first (consistent) example of a compact scattered space which is hereditarily separable and whose height is omega_2. It follows that its hereditary Lindelöf degree is aleph_2, showing the consistency of hL(K) can me strictly greater than the successor of hd(K) for compact spaces K. C(K_2) is the first consistent example of a Banach space of density aleph_2 without uncountable biorthogonal systems.
ASSUNTO(S)
espaços de banach c(k) sistema biortogonal hereditarily separable space espaços de asplund espaços hereditariamente separáveis espaços dispersos scattered space banach space c(k) forcing renormings renormações asplund space forcing biorthogonal system
