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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An extension of a theorem of Bessaga


Author: Charles A. Riley
Journal: Proc. Amer. Math. Soc. 48 (1975), 231-235
MSC: Primary 58B05; Secondary 46A15, 57A17
DOI: https://doi.org/10.1090/S0002-9939-1975-0402797-9
MathSciNet review: 0402797
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Abstract: In [1], C. Bessaga has shown that if $ X$ is a linear topological space admitting a weak incomplete norm $ w$ and $ A \subset X$ is closed in the $ w$-completion of $ X$, then $ A$ is negligible in $ X$. The present paper establishes this result in a space admitting a weak incomplete linear metric.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0402797-9
Keywords: Negligibility, shrinkable set, paranorm
Article copyright: © Copyright 1975 American Mathematical Society