Topology, isomorphic smoothness and polyhedrality in Banach spaces
Smith, Richard J.
46B03, 46B20, 46B26 | Mathematics - Functional Analysis
arxiv: Mathematics::Functional Analysis
In recent decades, topology has come to play an increasing role in some geometric aspects of Banach space theory. The class of so-called $w^*$-locally relatively compact sets was introduced recently by Fonf, Pallares, Troyanski and the author, and were found to be a useful topological tool in the theory of isomorphic smoothness and polyhedrality in Banach spaces. We develop the topological theory of these sets and present some Banach space applications.