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Point-set topology = a working textbook /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Point-set topology/ by Rafael López.
其他題名:	a working textbook /
作者:	López, Rafael.
出版者:	Cham :Springer International Publishing : : 2024.,
面頁冊數:	viii, 398 p. :ill. (some col.), digital ;24 cm.
內容註:	- Introduction -- Topological spaces -- Proximity on a topological space -- Metric spaces -- Continuity -- Homeomorphisms and topological invariants -- Product topology -- Connectedness -- Compactness -- Quotient topology -- The fundamental group.
Contained By:	Springer Nature eBook
標題:	Topology. -
電子資源:	https://doi.org/10.1007/978-3-031-58513-5
ISBN:	9783031585135

Point-set topology = a working textbook /
López, Rafael.

Point-set topologya working textbook /[electronic resource] :by Rafael López. - Cham :Springer International Publishing :2024. - viii, 398 p. :ill. (some col.), digital ;24 cm. - Springer undergraduate mathematics series,2197-4144. - Springer undergraduate mathematics series..

- Introduction -- Topological spaces -- Proximity on a topological space -- Metric spaces -- Continuity -- Homeomorphisms and topological invariants -- Product topology -- Connectedness -- Compactness -- Quotient topology -- The fundamental group.

This textbook offers a hands-on introduction to general topology, a fundamental tool in mathematics and its applications. It provides solid foundations for further study in mathematics in general, and topology in particular. Aimed at undergraduate students in mathematics with no previous exposure to topology, the book presents key concepts in a mathematically rigorous yet accessible manner, illustrated by numerous examples. The essential feature of the book is the large sets of worked exercises at the end of each chapter. All of the basic topics are covered, namely, metric spaces, continuous maps, homeomorphisms, connectedness, and compactness. The book also explains the main constructions of new topological spaces such as product spaces and quotient spaces. The final chapter makes a foray into algebraic topology with the introduction of the fundamental group. Thanks to nearly 300 solved exercises and abundant examples, Point-Set Topology is especially suitable for supplementing a first lecture course on topology for undergraduates, and it can also be utilized for independent study. The only prerequisites for reading the book are familiarity with mathematical proofs, some elements of set theory, and a good grasp of calculus.

ISBN: 9783031585135

Standard No.: 10.1007/978-3-031-58513-5doiSubjects--Topical Terms:

522026
Topology.

LC Class. No.: QA611

Dewey Class. No.: 514

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520 $a This textbook offers a hands-on introduction to general topology, a fundamental tool in mathematics and its applications. It provides solid foundations for further study in mathematics in general, and topology in particular. Aimed at undergraduate students in mathematics with no previous exposure to topology, the book presents key concepts in a mathematically rigorous yet accessible manner, illustrated by numerous examples. The essential feature of the book is the large sets of worked exercises at the end of each chapter. All of the basic topics are covered, namely, metric spaces, continuous maps, homeomorphisms, connectedness, and compactness. The book also explains the main constructions of new topological spaces such as product spaces and quotient spaces. The final chapter makes a foray into algebraic topology with the introduction of the fundamental group. Thanks to nearly 300 solved exercises and abundant examples, Point-Set Topology is especially suitable for supplementing a first lecture course on topology for undergraduates, and it can also be utilized for independent study. The only prerequisites for reading the book are familiarity with mathematical proofs, some elements of set theory, and a good grasp of calculus.
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