Topology [Paperback]

Contents: Introduction. - 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.Br|cker). - References. - Table of Symbols. -Index.Contents: Introduction. - 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.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. Fr?chet 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. Homotopywhat for?.- VI The Two Countability Axioms.- ?1. First and second countability axioms.- ?2. Infil#,