(pre-)Sheaves

Hello, I am trying to get my mind around (pre-)sheaves. I have studied point set topology in the past, but I didn't run into the notion of local homeomorphism. It seems to me that every local homeomorphism is a homeomorphism (because in a topological space (X, T), X is always a neighorhood of any point in X). Am I correct? Regards, Bill Halchin