目次

I. Introduction. 1. Introduction. II. Some Algebraic Topology. 2. Basic Metric Space Topology. 3. Forms and Curves. 4. The Jordan Curve Theorem. III. Deeper Topological Ideas. 5. Vector Spaces and Topology. 6. Locally Convex Spaces and Seminorms. 7. A New Look at Linear Functionals. 8. Deeper Results on Linear Functionals. 9. Stone–Weierstrass Results. IV. Topological Degree Theory. 10. Brouwer Degree Theory. 11 Leray–Schauder Degree. 12. Coincidence Degree. V. Manifolds. 13. Manifolds. 14. Smooth Functions on Manifolds. 15. The Global Structure of Manifolds. VI. Emerging Topologies. 16. Asynchronous Computation. 17. Signal Models and Autoimmune Disease. 18. Bar Code Computations in Consciousness Models. VII. Summing It All Up. 19. Summing It All Up. VIII. References. IX. Detailed Index.