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Simplicial Homomorphism


Let f:K^((0))->L^((0)) be a bijective correspondence such that the vertices v_0, ..., v_n of K span a simplex of K iff f(v_0), ..., f(v_n) span a simplex of L. Then the induced simplicial map g:|K|->|L| is a homeomorphism, and the map g is called a simplicial homeomorphism (Munkres 1993, p. 13).


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References

Hatcher, A. Algebraic Topology. Cambridge, England: Cambridge University Press, 2002.Munkres, J. R. Elements of Algebraic Topology. New York: Perseus Books Pub., 1993.

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Simplicial Homomorphism

Cite this as:

Weisstein, Eric W. "Simplicial Homomorphism." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SimplicialHomomorphism.html

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