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Nearrings of Continuous Functions From Topological Spaces into Topological Nearrings

Published online by Cambridge University Press:  20 November 2018

K. D. Magill Jr.
K. D. Magill Jr.*
Affiliation:
106 Diefendorf Hall, SUNY at Buffalo, Buffalo, NY14214-3093, USA, e-mail:mathmgil@ubvms.cc.buffalo.edu
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Abstract

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Let λ be a map from the additive Euclidean n-group Rn into the space R of real numbers and define a multiplication * on Rn by v * w = (λ(w))v. Then (Rn, + , *) is a topological nearring if and only if λ is continuous and λ(av) = aλ(v) for every v € Rn and every a in the range of λ. For any such map λ and any topological space X we denote by Nλ(X, Rn) the nearring of all continuous functions from X into (Rn, +, *) where the operations are pointwise. The ideals of Nλ(X, Rn) are investigated in some detail for certain λ and the results obtained are used to prove that two compact Hausdorff spaces X and Y are homeomorphic if and only if the nearrings Nλ(X, Rn) and Nλ(Y, Rn) are isomorphic.

Keywords

16Y3054H13
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 3 , 01 September 1996 , pp. 316 - 329
Copyright
Copyright © Canadian Mathematical Society 1996

References

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