Chapter: Sequences and Limits

This chapter deals with convergence of sets from a general, topological point of view. We will define limit points based solely on the basic concepts of topology, not relying on the concept of distance.

Examples: 1

  1. Definition: Isolated, Adherent, Limit, $\omega$-Accumulation and Condensation Points
  2. Definition: Sequence
  3. Definition: Carrier Set
  4. Definition: Subsequence
  5. Definition: Limits and Accumulation Points of Sequences
  6. Definition: Derived, Dense-in-itself, and Perfect Sets
  7. Proposition: Perfect Sets vs. Derived Sets
  8. Definition: Comparison of Filters, Finer and Coarser Filters
  9. Axiom: Filter
  10. Proposition: Filter Base
  11. Definition: Ultrafilter

Chapters: 1
Parts: 2

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  1. Steen, L.A.;Seebach J.A.Jr.: "Counterexamples in Topology", Dover Publications, Inc, 1970
  2. Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition