CH, a problem of Rolewicz and bidiscrete systems

Džamonja, Mirna and Juhász, István (2011) CH, a problem of Rolewicz and bidiscrete systems. Topology and its Applications, 158 (1). pp. 2485-2494. ISSN 1879-3207

[img]
Preview
PDF (newbidiscretev9.pdf)
Download (197kB) | Preview

Abstract

We give a construction under CH of a non-metrizable compact Hausdorff space K such that any uncountable ‘nice’ semi-biorthogonal sequence in C(K) must be of a very specific kind. The space K has many nice properties, such as being hereditarily separable, hereditarily Lindelöf and a 2-to-1 continuous preimage of a metric space, and all Radon measures on K are separable. However K is not a Rosenthal compactum. We introduce the notion of a bidiscrete system in a compact space K. These are subsets of K2 which determine biorthogonal systems of a special kind in C(K) that we call nice. We note that for every infinite compact Hausdorff space K, the space C(K) has a bidiscrete system and hence a nice biorthogonal system of size d(K), the density of K.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 10:19
Last Modified: 31 Oct 2019 13:24
URI: https://ueaeprints.uea.ac.uk/id/eprint/19972
DOI: 10.1016/j.topol.2011.08.005

Actions (login required)

View Item View Item