Cart
Free Shipping in Australia
Proud to be B-Corp

Topology S. Levy

Topology By S. Levy

Topology by S. Levy


Summary

- Fundamental Concepts. -Topological Vector Spaces.- The Quotient Topology. -Completion of Metric Spaces. - Homotopy. - The TwoCountability Axioms. - CW-Complexes. - Construction ofContinuous Functions on Topological Spaces. - CoveringSpaces. - The Theorem of Tychonoff. - Set Theory (by T. - References. - Table of Symbols.

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.

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.

Additional information

CIN1461270189G
9781461270188
1461270189
Topology by S. Levy
Used - Good
Paperback
Springer-Verlag New York Inc.
2012-10-03
193
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in good condition, but if you are not entirely satisfied please get in touch with us

Customer Reviews - Topology