Point-Set and Algebraic Topology
Academic (University) preparation with worked examples, written practice and independent learning assessments.
Independent university-level study of Point-Set and Algebraic Topology. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Topological spaces; Bases; Continuity; Homeomorphisms. Product topology; Quotient topology; Subspaces; Identification spaces. Compactness; Connectedness; Path connectedness; Local properties. Separation axioms; Countability; Metrization; Normal spaces. Homotopy; Fundamental group; Loop spaces; Homotopy equivalence. Covering spaces; Lifting properties; Deck transformations; Universal covers. Van Kampen theorem; Cell complexes; Surface groups; Classification examples. Simplicial complexes; Homology groups; Euler characteristic; Topological invariants. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required. Includes lessons, supplementary YouTube tutorials, practical exercises, quizzes and free/paid practice tests. Erudex is independent, not affiliated with the source institution or awarding body. Its 80% learning checks are not official grades or university credit. Content requires qualified subject review before use as a complete teaching programme.
Curriculum
One complete track with its own final exam and certificate.
Independent university-level study of Point-Set and Algebraic Topology. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Topological spaces; Bases; Continuity; Homeomorphisms. Product topology; Quotient topology; Subspaces; Identification spaces. Compactness; Connectedness; Path connectedness; Local properties. Separation axioms; Countability; Metrization; Normal spaces. Homotopy; Fundamental group; Loop spaces; Homotopy equivalence. Covering spaces; Lifting properties; Deck transformations; Universal covers. Van Kampen theorem; Cell complexes; Surface groups; Classification examples. Simplicial complexes; Homology groups; Euler characteristic; Topological invariants. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required.
Topological spaces; Bases; Continuity; Homeomorphisms
- Topological Spaces: Axiomatic Foundations, Closed Sets, and Neighborhood Operators Lab60 min
- Bases, Subbases, and Neighborhood Systems in Topology Lab60 min
- Continuity: Global Characterizations, Local Properties, and Boundary Behavior Lab60 min
- Homeomorphisms, Open and Closed Mappings, and Topological Equivalence Lab60 min