Question: A simplicial complex K is called a Kan complex if whenever every proper subset of a set of vertices S is included in K then

A simplicial complex K is called a Kan complex if whenever every proper subset of a set of vertices S is included in K then the set S must be included, i.e. form a simplex of K. Prove that the Rips complex Rt(P) is a Kan complex.

Is there anyone who is familiar with topology?

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