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

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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 (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 10:19
Last Modified:	12 Oct 2025 10:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/19972
DOI:	10.1016/j.topol.2011.08.005

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