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M-spaces with quasi-interior points

Published online by Cambridge University Press:  18 May 2009

W. A. Feldman  and
J. F. Porter
W. A. Feldman
Affiliation:
Mathematics Department, University of Arkansas, Fayetteville, Ar. 72701
J. F. Porter
Affiliation:
Mathematics Department, University of Arkansas, Fayetteville, Ar. 72701
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In this paper we characterize those locally convex lattices which can be represented as dense sublatices containing 1 in a space C(X) and whose topologies can be recognized as topologies of uniform convergence on selections of compact subsets of X. Here C(X) is the lattice of continuous real-valued functions on a completely regular space X. The class of such locally convex lattices includes the classical order unit spaces investigated by Kakutani [3], arbitrary products of order unit spaces, for example ∏ L∞ and the order partition spaces studied in [1].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 2 , July 1982 , pp. 131 - 135
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

REFERENCES

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