What are some hard books on topological groups? What are some hard books on general topology?

  • Topological Groups by M. F. Atiyah and I. G. MacDonald
  • Representation Theory of Compact Lie Groups by Harish-Chandra
  • Lectures on Harmonic Analysis by Elias M. Stein
  • Lie Groups and Lie Algebras by Jean Dieudonné
  • General Topology by John L. Kelley
  • Topology by James Dugundji
  • Real Analysis and Measure Theory by Vladimir Zorich
  • Introduction to Topology by Bert Mendelson
  1. What are some of the most important concepts in general topology?
  2. How can algebraic topology be used to study geometric shapes?
  3. What is the fundamental group of a space?
  4. What is the homology group of a space?
  5. What is the cohomology group of a space?
  • Discrete Mathematics and Its Applications by Kenneth Rosen
  • Topology by James Munkres
  • Abstract Algebra by I. N. Herstein
  • Principles of Mathematical Analysis by Walter Rudin
  • Mathematical Analysis by Tom Apostol

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