Geodesic
Nearrings of Continuous Functions From Topological Spaces into Topological Nearrings
Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 316-329

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1996-039-8
Mots-clés : 16Y30, 54H13 
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
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