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A Note on Polar Topologies

Published online by Cambridge University Press:  20 November 2018

J. M. Robertson  and
H. C. Wiser
J. M. Robertson
Affiliation:
Washington State University
H. C. Wiser
Affiliation:
Washington State University
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Let (E, E') be a dual pair and G be a collection of σ(E, E') bounded sets in E with the following properties:

  1. i) G contains all singletons.

  2. ii) If A, B are in G there is a C in G with A ∪B ⊆ C.

  3. iii) If A is in G then λ A ε G for any scaler λ.

Then sets of the form the polar of Ai, form base of neighbourhoods in E' for the polar topology TG of G convergence.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 4 , October 1968 , pp. 607 - 609
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Klee, V., On the Borelian and projective types of linear subspaces. Math. Scand. 6 (1958) 189-199.Google Scholar
2. Robertson, A.P. and Robertson, W.J., Topological vector spaces. (Cambridge University Press, 1964).Google Scholar
3. Schaefer, H. H., Topological vector spaces. (Macmillan Co., New York, 1966).Google Scholar