Nearrings of Continuous Functions From Topological Spaces into Topological Nearrings
Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 316-329
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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.
Jr., K. D. Magill. Nearrings of Continuous Functions From Topological Spaces into Topological Nearrings. Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 316-329. doi: 10.4153/CMB-1996-039-8
@article{10_4153_CMB_1996_039_8,
author = {Jr., K. D. Magill},
title = {Nearrings of {Continuous} {Functions} {From} {Topological} {Spaces} into {Topological} {Nearrings}},
journal = {Canadian mathematical bulletin},
pages = {316--329},
year = {1996},
volume = {39},
number = {3},
doi = {10.4153/CMB-1996-039-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-039-8/}
}
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