Topology

Author(s)

• Jänich, Klaus

Bibliographic Information

Topology

Klaus Jänich ; translated by Silvio Levy

（Undergraduate texts in mathematics）

Springer-Verlag, c1984

• : us
• : gw

Other Title

Topologie

Note

Translation of: Topologie

Bibliography: p. [177]-178

Includes index

Description and Table of Contents

Volume

: us ISBN 9780387908922

Description

Contents: Introduction. - Fundamental Concepts. - Topological Vector Spaces.- The Quotient Topology. - Completion of Metric Spaces. - Homotopy. - The Two Countability Axioms. - CW-Complexes. - Construction of Continuous Functions on Topological Spaces. - Covering Spaces. - The Theorem of Tychonoff. - Set Theory (by T. Br|cker). - References. - Table of Symbols. -Index.

Table of Contents

1. What is point-set topology about?.- 2. Origin and beginnings.- I Fundamental Concepts.- 1. The concept of a topological space.- 2. Metric spaces.- 3. Subspaces, disjoint unions and products.- 4. Bases and subbases.- 5. Continuous maps.- 6. Connectedness.- 7. The Hausdorff separation axiom.- 8. Compactness.- II Topological Vector Spaces.- 1. The notion of a topological vector space.- 2. Finite-dimensional vector spaces.- 3. Hilbert spaces.- 4. Banach spaces.- 5. Frechet spaces.- 6. Locally convex topological vector spaces.- 7. A couple of examples.- III The Quotient Topology.- 1. The notion of a quotient space.- 2. Quotients and maps.- 3. Properties of quotient spaces.- 4. Examples: Homogeneous spaces.- 5. Examples: Orbit spaces.- 6. Examples: Collapsing a subspace to a point.- 7. Examples: Gluing topological spaces together.- IV Completion of Metric Spaces.- 1. The completion of a metric space.- 2. Completion of a map.- 3. Completion of normed spaces.- V Homotopy.- 1. Homotopic maps.- 2. Homotopy equivalence.- 3. Examples.- 4. Categories.- 5. Functors.- 6. What is algebraic topology?.- 7. Homotopy-what for?.- VI The Two Countability Axioms.- 1. First and second countability axioms.- 2. Infinite products.- 3. The role of the countability axioms.- VII CW-Complexes.- 1. Simplicial complexes.- 2. Cell decompositions.- 3. The notion of a CW-complex.- 4. Subcomplexes.- 5. Cell attaching.- 6. Why CW-complexes are more flexible.- 7. Yes, but... ?.- VIII Construction of Continuous Functions on Topological Spaces.- 1. The Urysohn lemma.- 2. The proof of the Urysohn lemma.- 3. The Tietze extension lemma.- 4. Partitions of unity and vector bundle sections.- 5. Paracompactness.- IX Covering Spaces.- 1. Topological spaces over X.- 2. The concept of a covering space.- 3. Path lifting.- 4. Introduction to the classification of covering spaces.- 5. Fundamental group and lifting behavior.- 6. The classification of covering spaces.- 7. Covering transformations and universal cover.- 8. The role of covering spaces in mathematics.- X The Theorem of Tychonoff.- 1. An unlikely theorem?.- 2. What is it good for?.- 3. The proof.- Last Chapter Set Theory (by Theodor Broecker).- References.- Table of Symbols.

Volume

: gw ISBN 9783540908920

Description

An informal introduction to point set topology, which uses numerous illustrations to underline the arguments. The readers' intuition is tested throughout the text, as they progress to more advanced questions and problems.

Table of Contents

• Fundamental Concepts
• Topological Vector Spaces
• The Quotient Topology
• Completion of Metric Spaces
• Homotopy
• The Two Countability Axioms
• CW-Complexes
• Construction of Continuous Functions on Topological Spaces
• Covering Spaces
• The Theorem of Tychonoff
• Set Theory.

by "Nielsen BookData"

Details

• NCID: BA00429999
• ISBN:
  • 0387908927
  • 3540908927
• LCCN: 83014495
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: ger
• Place of Publication: New York
• Pages/Volumes: ix, 192 p.
• Size: 25 cm
• Classification:
  • LCC : QA611
  • DC19 : 514
  • NDC8 : 415.7
  • NDLC : MA81
• Subject Headings:
  • LCSH : Topology
• Parent Bibliography ID:
  • BA00018418