A simplicial complex 
is said to be locally finite if each vertex of 
belongs only to finitely many simplices
of 
.
Locally Finite Complex
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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.Referenced on Wolfram|Alpha
Locally Finite ComplexCite this as:
Weisstein, Eric W. "Locally Finite Complex." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LocallyFiniteComplex.html