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 |
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Faculty \ School: | Faculty of Science > School of Mathematics |

UEA Research Groups: | Faculty of Science > Research Groups > Logic |

Depositing User: | Vishal Gautam |

Date Deposited: | 18 Mar 2011 10:19 |

Last Modified: | 23 Oct 2022 00:31 |

URI: | https://ueaeprints.uea.ac.uk/id/eprint/19972 |

DOI: | 10.1016/j.topol.2011.08.005 |

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