Weakly continuous functions on Banach spaces not containing $l\sb 1$

0 O ct 1 99 2 WEAKLY LINDELOF DETERMINED BANACH SPACES NOT CONTAINING

The class of countably intersected families of sets is defined. For any such family we define a Banach space not containing l(N). Thus we obtain counterexamples to certain questions related to the heredity problem for W.C.G. Banach spaces. Among them we give a subspace of a W.C.G. Banach space not containing l(N) and not being itself a W.C.G. space. INTRODUCTION In the present paper we deal wit...

On Weakly Compact Subsets of Banach Spaces

Introduction. The two sections of this note are independent, but they are related by the fact that both use the results of [5 ] to obtain information on the properties of weakly compact sets in Banach spaces. In the first section we prove some results on a class of compact sets which is believed to include all weakly compact subsets of Banach spaces. We are interested in the properties of the n...

Holomorphic functions on Banach spaces

This is a survey about some problems from the theory of holomorphic functions on Banach spaces which have attracted the attention of many researchers during the last thirty years.

ON WEAKLY m-CONTINUOUS FUNCTIONS

In this paper we introduce a new notion of weakly m-continuous functions as functions from a set satisfying some minimal conditions into a topological spaces. We obtain some characterizations and several properties of such functions. Moreover, we define strongly m-closed graphs, m-compactness and m-connectedness and investigate the relationship between their properties and weakly m-continuous f...

Spaces of continuous functions into a Banach space