User:Alec/Questions to do/Algebraic topology/From books
From Maths
Questions
- Proposition 1.2 on page 2 (embarrassing) if the [ilmath]p[/ilmath]-simplex, [ilmath]s[/ilmath], is the convex hull of [ilmath]x_0,\ldots,x_p[/ilmath], then every point of [ilmath]s[/ilmath] has a distinct unique representation in the form [ilmath]\sum_it_ix_i[/ilmath] where [ilmath]t_i\ge 0[/ilmath] for all [ilmath]i[/ilmath] and [ilmath]\sum_it_i\eq 1[/ilmath][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.
- Exercise 1[2] 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)
