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This is on page 103 of Allen Hatcher's Algebraic Topology:

IT says "if we delete one of the n+1 vertices of an n-simplex $[v_0, ...,v_n]$ then the remaining n vertices span an (n-1)-simplex, called a face ..."

So, is this the same "span" in linear algebra. Suppose we take a 1-simplex, or also known as a triangle, remove one of its vertices, we have two vertices and it spans the entire Euclidean space since they are linearly independent.

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 No. Span in linear algebra means the linear span. Here, span means the convex hull. These should be enough for you to google. – darij grinberg Feb 13 2012 at 5:09

closed as not a real question by Will Jagy, Igor Pak, Andres Caicedo, Igor Rivin, Andy Putman Feb 13 2012 at 5:34

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