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Homomorphisms of near-rings of continuous real-valued functions

Published online by Cambridge University Press:  17 April 2009

K.D. Magill Jr
K.D. Magill Jr
Affiliation:
106 Diefendorf HallSUNY at BuffaloBuffalo, NY 14214–3093United States of America e-mail: mthmagil@ubvms.bitnetmthmagil@ubvms.cc.buffalo.edu
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Abstract

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For any topological near-ring (which is not a ring) whose additive group is the additive group of real numbers, we investigate the near-ring of all continuous functions, under the pointwise operations, from a compact Hausdorff space into that near-ring. Specifically, we determine all the homomorphisms from one such near-ring of functions to another and we show that within a rather extensive class of spaces, the endomorphism semigroup of the near-ring of functions completely determines the topological structure of the space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 3 , June 1996 , pp. 401 - 411
Copyright
Copyright © Australian Mathematical Society 1996

References

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