Overview

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.

Full Product Details

Author:   K. Jänich ,  S. Levy
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1984
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.326kg
ISBN:  

9781461270188

ISBN 10:   1461270189
Pages:   193
Publication Date:   03 October 2012
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

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. Fréchet 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 Bröcker).- References.- Table of Symbols.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions