Is the geometric realization of an abstract simplical complex locally finite?

I'm my understanding, an abstract complex need not be locally finite as long as the simplexes themselves are finite. And at the same time the geometric realization of each simplest is homeomorphic to a Euclidean simplex but it doesn't mean the realization is homeomorphic to a Euclidean complex.

I'm trying to understand this because to prove that a map between two geometric realizations of abstract complexes is continuous if its restriction to each realization is continuous. So I need to use the pasting lemma but for that I need to have that either the domain complex is finite or its realization is locally finite where neither one may be the case.