Free finitary algebras on compactly generated spaces

Publisher： Cambridge University Press

E-ISSN： 1755-1633|24|2|277-288

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.24, Iss.2, 1981-10, pp. : 277-288

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Abstract

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.

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