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Basic Topology 1
ISBN-13:
9789811665097
Veröffentl:
2022
Seiten:
502
Autor:
Avishek Adhikari
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone-Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand-Kolmogoroff theorem.
1. Prerequisites: Sets, Algebraic Systems, and Classical Analysis.- 2. Metric Spaces and Normed Linear Spaces.- 3. Topological Spaces and Continuous Maps.- 4. Separation Axioms.- 5. Compactness and Connectedness.- 6. Real-valued Continuous Functions.- 7. Countability, Separability and Embedding.- 8. Brief History of General Topology.
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