Special Course in Functional Analysis: (Non-)Commutative Topology
by Ville Turunen
Publisher: Aalto TKK 2008
Number of pages: 83
In this book you will learn something about functional analytic framework of topology. And you will get an access to more advanced literature on non-commutative geometry, a quite recent topic in mathematics and mathematical physics. The prerequisite for this course is some elementary understanding of Banach spaces.
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A sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. Contents: Sheaves; Sections; Cohomology groups of a space with coefficients in a presheaf; Introduction of the family Phi; etc.
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Many science and engineering problems can be rephrased as optimization problems on matrix search spaces endowed with a manifold structure. This book shows how to exploit the structure of such problems to develop efficient numerical algorithms.
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