What is the Acyclic Carrier Theorem and how can it be applied using chain maps?

[Socrates' Pen]

This is theorem 13.6 in Munkres' Elements of Algebraic Topology. I'm trying to go through this, but I can't prove it. Can someone do this one please?
Btw, its "Choose a partial ordering of the vertices of K that induces a linear ordering on the vertices of each simplex of K. Define \phi:C_p(K)\to C_p'(K) by letting \[\phi([v_0,...,v_p])=(v_0,...,v_p)\] if v_0<v_1<...<v_p in the given ordering. Define \psi:C_p'(K)\to C_p(K) by

\[\psi((w_0,...,w_p))=\begin{cases}[w_0,...,w_p] & \text{if the }w_i \text{ are distinct} \\ 0 * \text{otherwise} \end{cases} \]

Then \phi,\psi are augmentation-preserving chain maps that are chian homotopy inverses.
Thanks! The sooner the better of course, much appreciated. (Apply the acyclic carrier theorem)
<br /> \phi<br /> [\latex]

 

[Landau]

You have to end the latex-tag with /tex instead of \tex.

 

[Socrates' Pen]

THanks! Haha I was getting slightly annoyed, a simple mistake.
Now people can read it to help =)