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Loop space

In topology, a branch of mathematics, the loop space ΩX of a pointed topological space X is the space of (based) loops in X, i.e. continuous pointed maps from the pointed circle S1 to X, equipped with the compact-open topology. Two loops can be multiplied by concatenation. With this operation, the loop space is an A∞-space. That is, the multiplication is…

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TopologyMathematicsPointedTopological spaceContinuous
25 related topics

Eckmann–Hilton duality

SuspensionNaturalHomeomorphismHomotopy group
4 related topics

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Eckmann–Hilton duality

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Loop space

Nodes32
Edges31
Triples22
Avg. degree1.94
Density0.0625
Components1

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Loop space

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related to References · 17
Loop space → Adams, Annals, Berlin, BFb0067491, Infinite, ISBN, Iterated Loop Spaces, John Frank, Lecture Notes, Mathematics, Mathematics Studies, MR, New York, Peter, Princeton University Press, Springer-Verlag, The Geometry
related to Eckmann–Hilton duality · 5
Loop space → Eckmann, Hilton, Sigma, The, This

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loop space spaces topology displaystyle free circle group topological loops pointed set maps suspension eckmann hilton duality functor mathematics homotopy

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SubjectPredicateObjectConfidenceSrc
Loop spacerelated to Eckmann–Hilton dualityThe0.60section
Loop spacerelated to Eckmann–Hilton dualityEckmann0.60section
Loop spacerelated to Eckmann–Hilton dualityHilton0.60section
Loop spacerelated to Eckmann–Hilton dualitySigma0.60section
Loop spacerelated to Eckmann–Hilton dualityThis0.60section
Loop spacerelated to ReferencesAdams0.60section
Loop spacerelated to ReferencesJohn Frank0.60section
Loop spacerelated to ReferencesInfinite0.60section
Loop spacerelated to ReferencesAnnals0.60section
Loop spacerelated to ReferencesMathematics Studies0.60section
Loop spacerelated to ReferencesPrinceton University Press0.60section
Loop spacerelated to ReferencesISBN0.60section

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