Name: Topology By S. Levy
SKU: 9780387908922
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Topology Summary

Topology by S. Levy

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.

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.

Additional information

Sku

CIN0387908927A

ISBN 13

9780387908922

ISBN 10

0387908927

Title

Topology by S. Levy

Author

S. Levy

Series

Undergraduate Texts in Mathematics

Condition

Used - Well Read

Binding type

Hardback

Publisher

Springer-Verlag New York Inc.

Year published

19941206

Number of pages

193

Prizes

N/A

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Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

Note

This is a used book. We do our best to provide good quality books for you to read, but there is no escaping the fact that it has been owned and read by someone else previously. Therefore it will show signs of wear and may be an ex library book

Topology S. Levy

Topology by S. Levy

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Topology Summary

Topology by S. Levy

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