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Topological groups with co-monoid structures

Published online by Cambridge University Press:  18 May 2009

Elyahu Katz
Elyahu Katz
Affiliation:
Department of Mathematics, Haifa University, Haifa, Israel
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The Eckman–Hilton duality [4] reverses arrows in diagrams, turns products to co-products, and multiplications to co-multiplications, etc. In accordance with this process, Kan [5] obtained the dual of a monoid structure in the category of groups. In this way, we obtain co-monoid structures on topological groups. The main result of this paper is that for kaω groups (see §2), we obtain a one-to-one correspondence between the co-monoid structures, and the free topological bases of the group (§3), thus obtaining topological analogues of the main results of [5].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 2 , July 1977 , pp. 145 - 152
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

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