Assume that a piece-wise linear entity can be (heterogeneously) triangulated into a simplicial structure. Does not the underlying hypergraph (without the positional information of simplices) isomorphism class define all possible simplicial structures topologically equivalent to the original simplicial structure?
My answer to this question would be yes. But I do not know how to prove this claim. Is this a known concept? Or can there be a counter example? I am interested in this question because I want to be sure whether I correctly understand the concepts (up to now)
I have a related question on simplicial 'stuff'. What is the name of the most generic possibly heterogeneously dimensional piecewise linear entity that may not be connected? Namely an entitly composed of simplices in any arbitrary way. Can't we just call it 'simplicial'?