What is the definition of polygonal loop?

Question

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?"

Answer 1

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.