In this paper we characterize hereditarily-normal spaces in terms of the measure-theoretic properties of the lattice of closed sets. We then generalize from that lattice to other lattices. We apply the results to extremallydisconnected spaces.

s: Plenary Speakers Spiros Argyros (National Technical University of Athens, Greece) [email protected] HI extensions of L∞ spaces and spaces with very few operators Tuesday, July 30, HA4, 9:00–9:50 We will present a general method of embedding Banach spaces with separable dual into L∞ spaces admitting very few operators. In particular we will discuss the following two results. Theorem 1. (i...

We introduce notions of nearly good relations and N-sticky modulo a relation as tools for proving that spaces are D-spaces. As a corollary to general results about such relations, we show that Cp(X) is hereditarily a D-space whenever X is a Lindelöf Σ-space. This answers a question of Matveev, and improves a result of Buzyakova, who proved the same result for X compact. We also prove that if a ...

we introduce a new one-step iteration process to approximate common fixed points of twononexpansive mappings in banach spaces and prove weak convergence of the iterative sequence using (i)opial’s condition and (ii) kadec-klee property. strong convergence theorems are also established in banachspaces and uniformly convex banach spaces under the so-called condition ( a ), which is weaker thancom...