Loop Space
المؤلف:
Bredon, G.
المصدر:
Topology and Geometry New York: Springer-Verlag
الجزء والصفحة:
p. 456
15-5-2021
1823
Loop Space
Let 
be the set of continuous mappings 
. Then the topological space 
supplied with the compact-open topology is called a mapping space, and if 
is taken as the circle 
, then 
is called the "free loop space of 
" (or the space of closed paths).
If 
is a pointed space, then a basepoint can be picked on the circle and the mapping space 
of pointed maps can be formed. This space is denoted 
and is called the "loop space of 
."
REFERENCES:
Bredon, G. Topology and Geometry New York: Springer-Verlag, p. 456, 1993.
Brylinski, J.-L. Loop Spaces, Characteristic Classes and Geometric Quantization. Boston, MA: Birkhäuser, 1993.
Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 658, 1980.
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