Topology (Undergraduate Texts in Mathematics) - gebunden oder broschiert

EAN (ISBN-13): 9780387908922
ISBN (ISBN-10): 0387908927
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2007
Herausgeber: Springer
208 Seiten
Gewicht: 0,479 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2007-05-01T18:21:38+02:00 (Berlin)
Detailseite zuletzt geändert am 2024-05-08T19:56:29+02:00 (Berlin)
ISBN/EAN: 9780387908922

ISBN - alternative Schreibweisen:
0-387-90892-7, 978-0-387-90892-2
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: janich, jnich, jaenich, levy, klaus jänich
Titel des Buches: computer science, topology, computer notes, topologie, undergraduate text

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Daten vom Verlag:

Autor/in: K. Jänich
Titel: Undergraduate Texts in Mathematics; Topology
Verlag: Springer; Springer US
193 Seiten
Erscheinungsjahr: 1984-01-30
New York; NY; US
Übersetzer/in: S. Levy
Sprache: Englisch
58,84 € (DE)
60,49 € (AT)
65,00 CHF (CH)
Available
IX, 193 p.

BB; Hardcover, Softcover / Mathematik/Geometrie; Algebraische Topologie; Verstehen; CON_D026; Topologie; Topology; Algebraic Topology; BC

§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.