A topology on Milnor's group of a topological field and continuous joint determinants (Q1751514)

Summary: For the tuple set of commuting invertible matrices with coefficients in a given field, the joint determinants are defined as generalizations of the determinant map for the square matrices. We introduce a natural topology on Milnor's \(K\)-groups of a topological field as the quotient topology induced by the joint determinant map and investigate the existence of a nontrivial continuous joint determinant by utilizing this topology, generalizing the author's previous results [Linear Algebra Appl. 431, No. 9, 1633--1651 (2009; Zbl 1181.19001)] on the continuous joint determinants for the commuting invertible matrices over \(\mathbb{R}\) and \(\mathbb{C}\).