ASYMMETRIC NORMED BAIRE SPACE

Mohammed Bachir (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

We prove that an asymmetric normed space is never a Baire space if the topology induced by the asymmetric norm is not equivalent to the topology of a norm. More precisely, we show that a biBanach asymmetric normed space is a Baire space if and only if it is isomorphic to its associated normed space.

Keywords: Index of symmetry; Quasi-metric space; Asymmetric normed space; Baire space; 46B20; 46S99; 2010 Mathematics Subject Classification: 54E52

Domains: Functional Analysis [math.FA]

Mohammed Bachir. ASYMMETRIC NORMED BAIRE SPACE. 2021. ⟨hal-03223430v2⟩