Products of (weakly) discretely generated spaces

The McShane Integral in Weakly Compactly Generated Spaces

Di Piazza and Preiss asked whether every Pettis integrable function defined on [0, 1] and taking values in a weakly compactly generated Ba-nach space is McShane integrable. In this paper we answer this question in the negative.

Projections in Weakly Compactly Generated Banach Spaces and Chang’s Conjecture

Classical results on weakly compactly generated (WCG) Banach spaces imply the existence of projectional resolutions of identity (PRI) and the existence of many projections on separable subspaces (SCP). We address the questions if these can be the only projections in a nonseparable WCG space, in the sense that there is a PRI (Pα : ω ≤ α ≤ λ) such that any projection is the sum of an operator in ...

ε-weakly Chebyshev subspaces and quotient spaces

Weakly Continuously Urysohn Spaces

We study weakly continuously Urysohn spaces, which were introduced in [Z]. We show that every weakly continuously Urysohn w∆-space has a base of countable order, that separable weakly continuously Urysohn spaces are submetrizable, hence continuously Urysohn, that monontonically normal weakly continuously Urysohn spaces are hereditarily paracompact, and that no linear extension of any uncountabl...

On weakly bisequential spaces

Weakly bisequential spaces were introduced by A.V. Arhangel’skii [1], in this paper. We discuss the relations between weakly bisequential spaces and metric spaces, countably bisequential spaces, Fréchet-Urysohn spaces.