Definition of "barycenter"

Question

I have the following definition given:

(From "Introduction to algebraic topology" by Joseph J. Rotman)

Is the definition really meant like this? Or is $\frac{1}{m+1}(p_0+p_1+\dotso +p_m)$ meant?

For me it should read 1/(m+1) but the author (at least it seems to) writes "fractions" like this consistently: n/n+1 which is a little off.

So to be clear: For me $1/1+1=2$ and not $1/1+1=\frac{1}{2}$ as the author intends(?).

Answer 1

You are correct: the coefficient should be $\frac{1}{m+1}$; this particular bit of typesetting is appalling. It may be something that was done "in production" by someone trying to save vertical space in a text, who said "Hey, I can replace $\frac{A}{B}$ with $A/B$," and then applied this rule willy-nilly. Even so, the author should have objected when he saw the galley proofs. Sigh.