Metric Spaces

Vicente Montesinos (), Peter Zizler () and Václav Zizler ()
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Vicente Montesinos: Universitat Politècnica de València, Departamento de Matemática Aplicada Instituto de Matemática Pura y Aplicada
Peter Zizler: Mount Royal University, Department of Mathematics, Physics and Engineering
Václav Zizler: University of Alberta, Department of Mathematical and Statistical Sciences

Chapter 6 in An Introduction to Modern Analysis, 2015, pp 283-338 from Springer

Abstract: Abstract Geometry works, from ancient times, essentially with two instruments: a rule and a compass. The first one measures distances, the second, angles. Modern mathematics isolates these two activities in two subjects: metric spaces metric space (for a theory of distances) and inner product spaces inner product space (that presents a theory of angles or, if the reader prefers, orthogonality based in the notion of an inner product, also called a dot product dot product see{inner product} . Most interestingly, this notion—an inner product— is powerful enough to induce also a distance, and so the frame in which metric geometry can be done naturally is settled (see Sect. 11.1 ).

Keywords: Work Geometry; Textbf; Totally Bounded; Baire Category Theorem; Complete Metric (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-12481-0_6

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