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I am currently studying a classic on topology by Prof. James Dugundji entitled, 'TOPOLOGY', 2ed., 1996, 66-I0940 (LoCCCN - Library Resource).
It's quite technical and rich in mathematical ideas/definitions, etc. It's a slow read, and it may require years of intensive study to understand all of its contents.
Topics include:
I. Elementary Set Theory
II. Ordinals and Cardinals
III. Topological Spaces
IV. Cartesian Products
V. Connectedness
VI. Identification Topogy, Weak Topology
VII. Separation Axioms
VIII. Covering Axioms
IX. Metric Spaces
X. Convergence
XI. Compactness
XII. Function Spaces
XIII. The Spaces C(Y)
XIV. Complete Spaces
XV. Homotopy
XVI. Maps into Spheres
XVII. Topology of [tex]E^{n }[/tex]
XVIII. Homotopy Type
XIX. Path Spaces; H-Spaces
XX. Fiber Spaces
Appendix One: Vector Spaces; Polytopes
Appendix Two: Direct and Inverse Limits
Index
Enjoy!
