Buch, Englisch, 236 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 429 g
Reihe: De Gruyter Textbook
Metric Spaces, Dedekind Cut, Isometries, and Hilbert Cube
Buch, Englisch, 236 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 429 g
Reihe: De Gruyter Textbook
ISBN: 978-3-11-163606-1
Verlag: De Gruyter
This book is dedicated to metric spaces and their topology. The book starts with ZFC axioms. The real number system is constructed by both the Dedekind cut and the Cauchy sequence approach. The various examples and properties of metric spaces and normed linear spaces are discussed. The different distances between the sets are highlighted. The research work on metric-preserving maps and isometries on different p-norms has been discussed. Homeomorphism and different equivalent metrics have also been discussed. A detailed description of a metric on the product and the quotient set is also provided. The completion of a metric space as a universal property and applications of the Baire Category Theorem are covered. A special focus is on compactness and the relation between a compact metric space, the Hilbert Cube, and the Cantor set. The properties of connected and path-connected metric spaces are provided.
Zielgruppe
Graduate math students interested in applications to quantum phys
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
- Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
- Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Bauelemente, Schaltkreise
- Naturwissenschaften Physik Quantenphysik
- Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
- Mathematik | Informatik Mathematik Topologie
- Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
