Algebraic Topology · Problem 2.1.24

Homology — Allen Hatcher

Mathematics — Topology · barycentric-subdivision

Problem

Show that each

n

-simplex in the barycentric subdivision of

\Delta^n

is defined by

n

inequalities

t_{i_0} \leq t_{i_1} \leq \cdots \leq t_{i_n}

in its barycentric coordinates, where

(i_0, \cdots, i_n)

is a permutation of

(0, \cdots, n)