Geodesic
A characterization of determinants over topological fields
Glasgow mathematical journal, Tome 15 (1974) no. 1, pp. 60-62

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

Let K be a topological field. On introducing the vector-space topology on the n × n matrices over K, it becomes clear that the determinant map φ enjoys the following properties:(A) φ is a continuous surjective homomorphism from GLn(K) to K*,(B) φ(μa) = μn φ(a) for each non-zero φ in K, and all a in GLn(K). 
Odoni, R. W. K. A characterization of determinants over topological fields. Glasgow mathematical journal, Tome 15 (1974) no. 1, pp. 60-62. doi: 10.1017/S0017089500002123
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[3] 3.Neukirch, J., Klassenkörpertheorie (Mannheim, 1969). Google Scholar

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