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fresh_42

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- topology
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- a one dimensional space
- a connected, retractable space
- a graph of a function
- a segment of a circle
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Infrared

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If you have a singular chain ##\sigma\in C_n(X)##, not necessarily closed (as your "half circle" isn't), but its boundary is a chain in a subspace ##A\subset X##, then you can view ##\sigma## as representing a class in the relative homology group ##H_n(X,A).##

There is a similar notion for relative homotopy groups, where elements of ##\pi_n(X,A)## are (based) homotopy classes of maps ##(D^n,\partial D^n)\to (X,A)## such that ##\partial D^n## is mapped to ##A## throughout the homotopy.

There is a similar notion for relative homotopy groups, where elements of ##\pi_n(X,A)## are (based) homotopy classes of maps ##(D^n,\partial D^n)\to (X,A)## such that ##\partial D^n## is mapped to ##A## throughout the homotopy.

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WWGD

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