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 Title: Topological Groups: Yesterday, Today, Tomorrow
 Author(s) Sidney A. Morris (Editor)
 Publisher: Mdpi AG; 1. 2016 ed. edition (December 5, 2016)
 License(s): CC BY 4.0
 Hardcover: 228 pages
 eBook: PDF (230 pages)
 Language: English
 ISBN10: 3038422681
 ISBN13: 9783038422686
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Book Description
In 1900, David Hilbert asked whether each locally euclidean Topological Group admits a Lie group structure. This was the fifth of his famous 23 questions which foreshadowed much of the mathematical creativity of the twentieth century.
It required half a century of effort by several generations of eminent mathematicians until it was settled in the affirmative. These efforts resulted over time in the PeterWeyl Theorem, the Pontryaginvan Kampen Duality Theorem for locally compact abelian groups, and finally the solution of Hilbert 5 and the structure theory of locally compact groups, through the combined work of Andrew Gleason, Kenkichi Iwasawa, Deane Montgomery, and Leon Zippin.
For a presentation of Hilbert 5 see the 2014 book "Hilbert's Fifth Problem and Related Topics" by the winner of a 2006 Fields Medal and 2014 Breakthrough Prize in Mathematics, Terence Tao.
About the Authors N/A
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