Hatcher 2.1.23

Hatcher, Algebraic Topology, Chapter 2, Section 1

23. Show that the second barycentric subdivision of a \Delta-complex is a simplicial complex. Namely, show that the first barycentric subdivision produces a \Delta-complex with the property that each simplex has all its vertices distinct, then show that for a \Delta-complex with this property, barycentric subdivision produces a simplicial complex.
Proof.

\square

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