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BORNOLOGICAL COUNTABLE ENLARGEMENTS

Published online by Cambridge University Press:  27 January 2003

Ian Tweddle  and
S. A. Saxon
Ian Tweddle
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, UK ([email protected])
S. A. Saxon
Affiliation:
Department of Mathematics, University of Florida, PO Box 118105, Gainesville, FL 32611-8105, USA ([email protected])
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Abstract

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We show that for a non-flat bornological space there is always a bornological countable enlargement; moreover, when the space is non-flat and ultrabornological the countable enlargement may be chosen to be both bornological and barrelled. It is also shown that countable enlargements for barrelled or bornological spaces are always Mackey topologies, and every quasibarrelled space that is not barrelled has a quasibarrelled countable enlargement.

AMS 2000 Mathematics subject classification: Primary 46A08; 46A20

Keywords

countable enlargementbornological spacequasibarrelled spaceMackey topology
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 1 , February 2003 , pp. 35 - 44
Copyright
Copyright © Edinburgh Mathematical Society 2003