A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants
2017 ◽
Vol 2017
◽
pp. 1-5
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 on the continuous joint determinants for the commuting invertible matrices over R and C.
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1990 ◽
Vol 05
(19)
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pp. 3777-3786
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1991 ◽
Vol 06
(20)
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pp. 3571-3598
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2017 ◽
Vol 29
(05)
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pp. 1750015
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2009 ◽
Vol 823
(3)
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pp. 403-427
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