Hatcher 2.1.24

Hatcher, Algebraic Topology, Chapter 2, Section 1

24. 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,\ldots,i_n) is a permutation of (0,\ldots,n).
Proof.

\square

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