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A generalized inductive limit topology for linear spaces

Published online by Cambridge University Press:  18 May 2009

S. O. Iyahen  and
J. O. Popoola
S. O. Iyahen
Affiliation:
University of Benin, Benin City, Nigeria
J. O. Popoola
Affiliation:
College of Education, University of Lagos, Lagos, Nigeria
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In the usual definition of an inductive limit of locally convex spaces, one is given a linear space E, a family (Eα) of locally convex spaces and a set (iα) of linear maps from Eα into E. Garling in [2] studies an extension of this, looking at absolutely convex subsets Sα of Eα and restrictions jα of iα to such sets. If, in the definition of Garling [2, p. 3], each Sα is instead a balanced semiconvex set, then the finest linear (not necessarily locally convex) topology on E for which the maps ja are continuous, will be referred to as the generalized *-inductive limit topology of the semiconvex sets. This topology is our object of study in the present paper; we find applications in the closed graph theorem.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 2 , September 1973 , pp. 105 - 110
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

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