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Point-set topologya working textbook /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Point-set topologyby Rafael López.
Reminder of title:	a working textbook /
Author:	López, Rafael.
Published:	Cham :Springer International Publishing :2024.
Description:	viii, 398 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Topology.
Online resource:	https://doi.org/10.1007/978-3-031-58513-5
ISBN:	9783031585135$q(electronic bk.)

Point-set topologya 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$q(electronic bk.)

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

185965
Topology.

LC Class. No.: QA611

Dewey Class. No.: 514

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490 1 $a Springer undergraduate mathematics series, $x 2197-4144
505 0 $a - Introduction -- Topological spaces -- Proximity on a topological space -- Metric spaces -- Continuity -- Homeomorphisms and topological invariants -- Product topology -- Connectedness -- Compactness -- Quotient topology -- The fundamental group.
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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