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Universal arrows to forgetful functors from categories of topological algebra

Published online by Cambridge University Press:  17 April 2009

Vladimir G. Pestov
Vladimir G. Pestov
Affiliation:
Department of Mathematics Victoria, University of Wellington, PO Box 600 Wellington, New Zealandvladimir.pestov@vuw.ac.nz
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We survey the present trends in theory of universal arrows to forgetful functors from various categories of topological algebra and functional analysis to categories of topology and topological algebra. Among them are free topological groups, free locally convex spaces, free Banach-Lie algebras, and more. An accent is put on the relationship of those constructions with other areas of mathematics and their possible applications. A number of open problems is discussed; some of them belong to universal arrow theory, and other may become amenable to the methods of this theory.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 2 , October 1993 , pp. 209 - 249
Copyright
Copyright © Australian Mathematical Society 1993

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