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Equational Compactness of G-Sets

Published online by Cambridge University Press:  20 November 2018

B. Banaschewski
B. Banaschewski*
Affiliation:
McMaster University
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This paper deals with the notion of equational compactness and related concepts in the special case of G-sets for an arbitrary group G. It provides characterizations of pure extensions, pure-essential extensions, and equational compactness in terms of the stability groups of a G-set, proves the general existence of equationally compact hulls, and gives an explicit description of these. Further, it establishes, among other results, that all G-sets are equationally compact iff all subgroups of the group G are finitely generated, that every equationally compact G-set is a retract of a topologically compact one, and that for free groups G with infinite basis there are homogeneous G-sets which are not equationally compact.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 11 - 18
Copyright
Copyright © Canadian Mathematical Society 1974

References

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