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On various types of barrelledness and the hereditary property of (DF)-spaces

Published online by Cambridge University Press:  18 May 2009

T. Husain  and
Yau-Chuen Wong
T. Husain
Affiliation:
Department of Mathematics, McMaster University, Hamilton, Ontario, Canada
Yau-Chuen Wong
Affiliation:
Department of Mathematics, United College, Chinese University of Hong Kong, Hong Kong
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Recently, Levin and Saxon [5], De Wilde and Houet [2] defined the σ-barrelledness while Husain [3] defined the countable barrelledness and countable quasibarrelledness. It is well-known that barrelled spaces are countably barrelled, and countably barrelled spaces are σ-barrelled. It is natural to ask whether there is some condition for σ-barrelled (resp. countably barrelled) spaces to be countably barrelled (resp. barrelled). Using the concept of S-absorbent sequences of sets, we are able to give such conditions in Theorem 2.5 and Corollaries 2.6 and 2.7.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 17 , Issue 2 , July 1976 , pp. 134 - 143
Copyright
Copyright © Glasgow Mathematical Journal Trust 1976

References

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