### 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.

Original language | English |
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Pages (from-to) | 277-288 |

Number of pages | 12 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 24 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1981 |

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## Cite this

Day, B. J. (1981). Free finitary algebras on compactly generated spaces.

*Bulletin of the Australian Mathematical Society*,*24*(2), 277-288. https://doi.org/10.1017/S0004972700007644