Topology

(Autor)

Buch | Hardcover
193 Seiten
1984
Springer-Verlag New York Inc.
978-0-387-90892-2 (ISBN)

Lese- und Medienproben

Topology - K. Janich
58,84 inkl. MwSt
- 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.
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. 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.

Reihe/Serie Undergraduate Texts in Mathematics
Übersetzer S. Levy
Zusatzinfo IX, 193 p.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Geometrie / Topologie
Medizin / Pharmazie Gesundheitsfachberufe MTA - Radiologie
ISBN-10 0-387-90892-7 / 0387908927
ISBN-13 978-0-387-90892-2 / 9780387908922
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Wie bewerten Sie den Artikel?
Bitte geben Sie Ihre Bewertung ein:
Bitte geben Sie Daten ein:
Mehr entdecken
aus dem Bereich
Mathematik 2; Print inkl. eLehrmittel

von Benno Jakob; Hans Marthaler; Katharina Schudel

Buch | Softcover (2020)
hep verlag
61,00