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The Resource Elementary point-set topology : a transition to advanced mathematics, André L. Yandl, Seattle University; Adam Bowers, University of California San Diego

Elementary point-set topology : a transition to advanced mathematics, André L. Yandl, Seattle University; Adam Bowers, University of California San Diego

Label
Elementary point-set topology : a transition to advanced mathematics
Title
Elementary point-set topology
Title remainder
a transition to advanced mathematics
Statement of responsibility
André L. Yandl, Seattle University; Adam Bowers, University of California San Diego
Creator
Contributor
Author
Subject
Language
eng
Summary
In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses. Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations
Cataloging source
np
http://library.link/vocab/creatorName
Yandl, André L
Dewey number
514/.322
Illustrations
illustrations
Index
index present
LC call number
QA603
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
Bowers, Adam
Series statement
  • Aurora Dover modern math originals
  • Dover Books on mathematics
http://library.link/vocab/subjectName
  • Point set theory
  • Propositional calculus
  • Topology
  • Calculus
Label
Elementary point-set topology : a transition to advanced mathematics, André L. Yandl, Seattle University; Adam Bowers, University of California San Diego
Instantiates
Publication
Copyright
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1 Mathematical Proofs and Sets -- 1.1 Introduction to Elementary Logic -- 1.2 More Elementary Logic -- 1.3 Quantifiers -- 1.4 Methods of Mathematical Proof -- 1.5 Introduction to Elementary Set Theory -- 1.6 Cardinality -- 1.7 Cardinal Arithmetic -- 2 Topological Spaces -- 2.1 Introduction -- 2.2 Topologies -- 2.3 Bases -- 2.4 Subspaces -- 2.5 Interior, Closure, and Boundary -- 2.6 Hausdorff spaces -- 2.7 Metric Spaces -- 2.8 Euclidean Spaces -- 3 Continuous Functions
  • 3.1 Review of the Function Concept -- 3.2 More on Image and Inverse Image -- 3.3 Continuous Functions -- 3.4 More on Continuous Functions -- 3.5 More on Homeomorphism -- 4 Product Spaces -- 4.1 Products of Sets -- 4.2 Product Spaces -- 4.3 More on Product Spaces -- 5 Connectedness -- 5.1 Introduction to Connectedness -- 5.2 Products of Connected Spaces -- 5.3 Connected Subsets of the Real Line -- 6 Compactness -- 6.1 Introduction to Compactness -- 6.2 Compactness in the Space of Real Numbers -- 6.3 The Product of Compact Spaces -- 6.4 Compactness in Metric Spaces
  • 6.5 More on Compactness in Metric Spaces -- 6.6 The Cantor Set -- 7 Fixed Point Theorems and Applications -- 7.1 Sperner's Lemma -- 7.2 Brouwer's Fixed Point Theorem -- 7.3 The Fundamental Theorem of Algebra -- 7.4 Function Spaces -- 7.5 Contractions
Dimensions
23 cm.
Extent
254 pages
Isbn
9780486803494
Lccn
2015050597
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
Label
Elementary point-set topology : a transition to advanced mathematics, André L. Yandl, Seattle University; Adam Bowers, University of California San Diego
Publication
Copyright
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1 Mathematical Proofs and Sets -- 1.1 Introduction to Elementary Logic -- 1.2 More Elementary Logic -- 1.3 Quantifiers -- 1.4 Methods of Mathematical Proof -- 1.5 Introduction to Elementary Set Theory -- 1.6 Cardinality -- 1.7 Cardinal Arithmetic -- 2 Topological Spaces -- 2.1 Introduction -- 2.2 Topologies -- 2.3 Bases -- 2.4 Subspaces -- 2.5 Interior, Closure, and Boundary -- 2.6 Hausdorff spaces -- 2.7 Metric Spaces -- 2.8 Euclidean Spaces -- 3 Continuous Functions
  • 3.1 Review of the Function Concept -- 3.2 More on Image and Inverse Image -- 3.3 Continuous Functions -- 3.4 More on Continuous Functions -- 3.5 More on Homeomorphism -- 4 Product Spaces -- 4.1 Products of Sets -- 4.2 Product Spaces -- 4.3 More on Product Spaces -- 5 Connectedness -- 5.1 Introduction to Connectedness -- 5.2 Products of Connected Spaces -- 5.3 Connected Subsets of the Real Line -- 6 Compactness -- 6.1 Introduction to Compactness -- 6.2 Compactness in the Space of Real Numbers -- 6.3 The Product of Compact Spaces -- 6.4 Compactness in Metric Spaces
  • 6.5 More on Compactness in Metric Spaces -- 6.6 The Cantor Set -- 7 Fixed Point Theorems and Applications -- 7.1 Sperner's Lemma -- 7.2 Brouwer's Fixed Point Theorem -- 7.3 The Fundamental Theorem of Algebra -- 7.4 Function Spaces -- 7.5 Contractions
Dimensions
23 cm.
Extent
254 pages
Isbn
9780486803494
Lccn
2015050597
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations

Library Locations

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      185 Larkfield Road, East Northport, NY, 11731, US
      40.878082 -73.324623
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