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.
Table of Contents
Examples: 1
- Definition: Isolated, Adherent, Limit, $\omega$-Accumulation and Condensation Points
- Definition: Sequence
- Definition: Carrier Set
- Definition: Subsequence
- Definition: Limits and Accumulation Points of Sequences
- Definition: Derived, Dense-in-itself, and Perfect Sets
- Proposition: Perfect Sets vs. Derived Sets
- Definition: Comparison of Filters, Finer and Coarser Filters
- Axiom: Filter
- Proposition: Filter Base
- Definition: Ultrafilter
Mentioned in:
Chapters: 1
Parts: 2
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References
Bibliography
- Steen, L.A.;Seebach J.A.Jr.: "Counterexamples in Topology", Dover Publications, Inc, 1970
- Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition