Abstract
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).
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