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On the Structure of Locally Solid Topologies

Published online by Cambridge University Press:  20 November 2018

C. D. Aliprantis  and
O. Burkinshaw
C. D. Aliprantis
Affiliation:
Department of Mathematical Sciences Indiana University & Purdue University at Indianapolis Indianapolis, Indiana46205
O. Burkinshaw
Affiliation:
Department of Mathematical Sciences Indiana University & Purdue University at Indianapolis Indianapolis, Indiana46205
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This paper considers what conditions on the order structure of a Riesz space will insure that one locally solid topology is finer than another, or when does one topology induce a finer topology than another on the order bounded subsets. The basic tool employed for the comparisons will be the carrier of a locally solid topology. We shall deal mainly with topologies whose carriers are order dense; a locally solid topology with order dense carrier will be called entire.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 2 , 01 June 1980 , pp. 185 - 191
Copyright
Copyright © Canadian Mathematical Society 1980

References

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