Topology Through Definitions : Meaning, Structure, and Proof
Published by Pax Academia
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
AbeBooks seller since August 14, 2006
Condition: New
US$ 85.22
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nach der Bestellung gedruckt Neuware - Printed after ordering - Topology Through Definitions: Meaning, Structure, and Proof is a definition-led introduction to elementary topology designed to help students understand not only what topological concepts mean, but how those definitions shape mathematical reasoning and proof.Rather than treating definitions as formal statements to memorize, the book develops each major idea through interpretation, examples, diagrams, proof strategies, and exercises. Topics include topological spaces, open and closed sets, neighborhoods, interior, closure, boundary, exterior, limit points, isolated points, density, bases and subbases, continuity, homeomorphisms, subspace and product topologies, open and closed maps, and quotient topology.The text places particular emphasis on the relationships among these concepts. Readers are encouraged to see how interior and closure contrast, how boundary connects a set with its complement, how accumulation behavior shapes closure, and how continuity emerges from the preservation of open-set structure through inverse images.Written for students encountering topology for the first time, the book may be used as a companion to a traditional topology course, as a preparatory text before studying a more advanced textbook, or as a self-study guide for independent learners. Its goal is to make abstract definitions usable by showing how they organize examples, clarify misconceptions, and suggest proof strategies.The central theme is simple: in topology, definitions are not merely preliminary vocabulary. They are the structure from which the subject grows.…
Seller Inventory # 9798182803823
- Title
- Topology Through Definitions : Meaning, Structure, and Proof
- Author
- Michael Paxinos
- Publisher
- Pax Academia
- Condition
- Neu
- Binding
- Buch
- ISBN 13
- 9798182803823
- Item weight
- 1,347 grams
- Dimensions
- 286x221x23 mm
Topology Through Definitions: Meaning, Structure, and Proof is a definition-led introduction to elementary topology designed to help students understand not only what topological concepts mean, but how those definitions shape mathematical reasoning and proof.
Rather than treating definitions as formal statements to memorize, the book develops each major idea through interpretation, examples, diagrams, proof strategies, and exercises. Topics include topological spaces, open and closed sets, neighborhoods, interior, closure, boundary, exterior, limit points, isolated points, density, bases and subbases, continuity, homeomorphisms, subspace and product topologies, open and closed maps, and quotient topology.
The text places particular emphasis on the relationships among these concepts. Readers are encouraged to see how interior and closure contrast, how boundary connects a set with its complement, how accumulation behavior shapes closure, and how continuity emerges from the preservation of open-set structure through inverse images.
Written for students encountering topology for the first time, the book may be used as a companion to a traditional topology course, as a preparatory text before studying a more advanced textbook, or as a self-study guide for independent learners. Its goal is to make abstract definitions usable by showing how they organize examples, clarify misconceptions, and suggest proof strategies.
The central theme is simple: in topology, definitions are not merely preliminary vocabulary. They are the structure from which the subject grows.
"Synopsis" may belong to another edition of this title.
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"About the title" may belong to another edition of this title.
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