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Free finitary algebras on compactly generated spaces

Published online by Cambridge University Press:  17 April 2009

Brian J. Day
Brian J. Day
Affiliation:
School of Mathematics and Physics, Macquarie University, North Ryde, New South Wales 2113, Australia.
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Abstract

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An explicit colimit formula is used to describe the free k-space algebra on a given k-space for any k-enriched finitary theory. A question, raised and solved affirmatively by several authors, has been that of whether the free k-space group on a weakly hausdorff k-space is again weakly hausdorff and admits a closed embedding of the generators. In the present article both these features of finitary k-space algebra are combined to answer analogous questiona regarding the free finitary k-space algebras in general, and the weakly hausdorff separation axiom. Relationships with other problems in k-space theory are described.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 2 , October 1981 , pp. 277 - 288
Copyright
Copyright © Australian Mathematical Society 1981

References

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