User:Alec/Questions to do/Algebraic topology/From books

Questions

1. Proposition 1.2 on page 2 (embarrassing) if the $p$-simplex, $s$, is the convex hull of $x_0,\ldots,x_p$, then every point of $s$ has a distinct unique representation in the form $\sum_it_ix_i$ where $t_i\ge 0$ for all $i$ and $\sum_it_i\eq 1$ Alec (talk) 23:19, 23 January 2017 (UTC)
   • The unique part isn't so bad using proposition 1.1, however showing that each point has such a representation is difficult.
2. Exercise 1 would be good too. I've had a look at it and get the gist, but only informally Alec (talk) 23:19, 23 January 2017 (UTC)