Abstract

Learn Topology

Geometry without distance. What survives when you bend and stretch a shape without tearing it.

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Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

40 lessons in Topology

Metric spacesOpen sets & continuityCompactness & connectednessContinuous maps & homeomorphismsConnectednessFundamental group introQuotient spaces & gluingSeparation axiomsProduct & subspace topologyCompleteness & Banach fixed pointCovering spacesManifold theory introDifferential forms & de Rham cohomologyHigher homotopy groupsKnot theory introProof: continuous image of compact is compactProof: connected ⟹ continuous image connectedProof: IVT from connectednessAlgebraic topology computationsSimplicial complexes & homology introUrysohn's lemma & metrizationVan Kampen's theoremClassification of surfacesSingular homology & cohomologyTychonoff's theoremCharacterizations of compactnessNets & filtersHomotopy equivalence & deformation retractsCW complexesDegree theory & Brouwer's fixed point theoremThe Borsuk–Ulam theoremEuler characteristic & Betti numbersExact sequences & the LES of a pairThe Mayer–Vietoris sequenceCup product & the cohomology ringPoincaré dualityFiber bundles & fibrationsVector bundles & characteristic classesThe Hurewicz theoremMorse theory
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Topology exactly where it's useful.

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Related Abstract subjects
Abstract AlgebraRepresentation TheoryDifferential GeometryCommutative Algebra & Algebraic Geometry