2009/10/16 by Mirna Džamonja, MIrna Dzamonja, Dzamonja, MIrna +3
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #math.GN #math.LO
paper · pdf · doi:10.48550/arxiv.0910.3091
openalex publication_date 2009/10/16 · arxiv created 2009/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a construction under CH of a non-metrizable compact Hausdorff space K such that any uncountable 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 bidiscrete systems in compact spaces and note that every infinite compact Hausdorff space K must have a bidiscrete system of size d(K), the density of K. This, in particular, implies that C(K) has a biorthogonal system of size d(K).