Course

General topology

Course under construction · 32 of 33 concepts published; more are added as they are reviewed.

Study metric and topological spaces: open sets, continuity, connectedness and compactness. It gives the common language of analysis, geometry and much of modern mathematics.

32concepts

5topics

320exercises

≈ 16 hof study approx.

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Course path

1
Metric spaces 5 concepts
Metric space · Open ball · Open set in a metric space · Convergence in a metric space · Complete metric space
2
Topological spaces 10 concepts
Topology · Topological space · Discrete and trivial topology · Closed set · Basis of a topology · Neighborhood of a point · Interior of a set · Closure of a set · Boundary of a set · Accumulation point
3
Continuity and constructions 5 concepts
Continuous function between topological spaces · Homeomorphism · Subspace topology · Product topology · Quotient topology
4
Separation and connectedness 5 concepts
Hausdorff space · Connected space · Continuous image of a connected space · Path-connected space · Connected component
5
Compactness 7 concepts
Open cover · Compact space · Compact sets in Hausdorff spaces · Continuous image of a compact space · Heine-Borel theorem · Sequential compactness · Lebesgue number

Sources

James R. Munkres, Topology, 2nd edition, Pearson, 2000.
Bert Mendelson, Introduction to Topology, 3rd edition, Dover Publications, 1990.
Stephen Willard, General Topology, Dover reprint, Dover Publications, 2004.