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Stability and closed graph theorems in classes of bornological spaces

Published online by Cambridge University Press:  18 May 2009

T. K. Mukherjee  and
W. H. Summers
T. K. Mukherjee
Affiliation:
Department of Mathematics, Jadavpur University, Calcutta-700009, India
W. H. Summers
Affiliation:
Department of Mathematics, University of Arkansas, Fayetteville, AR 72701, USA
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In the general theory of locally convex spaces, the idea of inductive limit is pervasive, with quotient spaces and the less obvious notion of direct sum being among the instances. Bornological spaces provide another important example. As is well known (cf. [7]), a Hausdorff locally convex space E is bornological if, and only if, E is an inductive limit of normed vector spaces. Going even further in this direction, a complete Hausdorff bornological space is an inductive limit of Banach spaces.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 2 , July 1982 , pp. 151 - 162
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

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