Concepts
Manifold
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A manifold is a topological space that locally resembles Euclidean space near each point, so that a manifold's global structure can be complicated even though every small neighbourhood around any point looks like ordinary flat space.
Facts
Cross-Tradition Connections
Sources
1. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and StatisticsRiemann biography, 1854 habilitation lectureQuote, Riemann biography, 1854 habilitation lecture
Riemann's lecture Ueber die Hypothesen welche der Geometrie zu Grunde liegen, delivered on 10 June 1854, became a classic of mathematics.
Manifold (Wikipedia)
Wikimedia Foundationlead paragraphQuote, lead paragraph
a manifold is a topological space that locally resembles Euclidean space near each point
Manifold (Wikipedia)
Wikimedia FoundationAssociated With: Bernhard Riemann, history sectionQuote, Associated With: Bernhard Riemann, history section
Riemann was the first one to do extensive work generalizing the idea of a surface to higher dimensions.
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