A Primer on Hilbert Space Theory: Metric Spaces
Alabiso, Carlo; Weiss, Ittay
2014-10-09 00:00:00
[This chapter is concerned with the basic concepts of metric spaces and results that are most relevant to applications in Hilbert space theory. Assuming no prior knowledge of metric spaces, the definitions are given in detail and the relation to normed spaces made explicit early on. The main theorems proved are the Banach Fixed-Point Theorem, Baire’s Theorem, the equivalence between compact sets and complete totally bounded sets, and an account of completion.]
http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.pnghttp://www.deepdyve.com/lp/springer-journals/a-primer-on-hilbert-space-theory-metric-spaces-1ORFe6Y58V
[This chapter is concerned with the basic concepts of metric spaces and results that are most relevant to applications in Hilbert space theory. Assuming no prior knowledge of metric spaces, the definitions are given in detail and the relation to normed spaces made explicit early on. The main theorems proved are the Banach Fixed-Point Theorem, Baire’s Theorem, the equivalence between compact sets and complete totally bounded sets, and an account of completion.]
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