• 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
• ISBN-10: 3038422681
• ISBN-13: 978-3038422686
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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 Peter-Weyl Theorem, the Pontryagin-van 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.

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• Geometry and Topology
• Algebra, Abstract Algebra, and Linear Algebra, etc.
• Calculus and Mathematical Analysis (Real Analysis, Functional Analysis, etc.)
• Category Theory

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