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Asymmetric Normed Baire Space

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Abstract

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.

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Acknowledgements

This research has been conducted within the FP2M federation (CNRS FR 2036) and SAMM Laboratory of the University Paris Panthéon-Sorbonne.

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  1. Laboratoire SAMM 4543, Centre P.M.F. 90 rue Tolbiac, Université Paris 1 Panthéon-Sorbonne, 75634, Paris cedex 13, France

    Mohammed Bachir

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  1. Mohammed Bachir
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Correspondence to Mohammed Bachir.

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Bachir, M. Asymmetric Normed Baire Space. Results Math 76, 176 (2021). https://doi.org/10.1007/s00025-021-01483-6

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  • DOI: https://doi.org/10.1007/s00025-021-01483-6

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