How to prove "every loop can be uniformly approximated arbitrarily closed by a quotient of polynomial loops?" In Blackadar's book, the proof is completed with the help of "polygonal loops," but what is the definition of "polygonal loops?"
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Have you checked the index of Blackadar's book for polygonal loops? – N. F. Taussig Apr 16 '15 at 23:56
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I have checked,the definion is not given! – math112358 Apr 17 '15 at 00:02
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I would suppose that a polygonal loop is a loop in the form of a polygon. – Apr 17 '15 at 02:09
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I'm fairly sure polygonal loop here means piecewise linear. The proofs in Blackadar can be pretty vague.
For a more detailed proof see either:
Lemma 11.2.3 in "An introduction to K-theory for C*-algebras" - Rordam, Larsen & Lausten; or
Lemma 9.2.4 in "K-theory and C*-algebras" - Wegge-Olsen.
Zorngo
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But in Blackadar's book ,A is a local Banach algebra,while In Olsen's book and Rodam's book.A is assumed to be a C* algebra! – math112358 Apr 18 '15 at 05:54
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True, but I don't imagine this particular proof relies on the C*-identity in any way. It should be fairly easily transferable. – Zorngo Apr 18 '15 at 06:12
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