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An unpleasant set in a non-locally-convex vector lattice

Published online by Cambridge University Press:  20 January 2009

J. D. Pryce
J. D. Pryce
Affiliation:
University of Aberdeen
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In a linear topological space E one often carries out various “ smoothing ” operations on a subset A, such as taking the convex hull co A and the closure A-. If E is also a (real) vector lattice, the solid hull

is also a natural “ smoothing out ” of A. If sol A = A then A is called solid, and if E has a base of solid neighbourhoods of 0 as do all the common topological vector lattices such as C(X), Lp, Köthe spaces and so on—then E is called a locally solid space.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 3 , June 1973 , pp. 229 - 233
Copyright
Copyright © Edinburgh Mathematical Society 1973

References

REFERENCES

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