A topological variation of the reconstruction conjecture

This paper investigates topological reconstruction, related to the reconstruction conjecture in graph theory. We ask whether the homeomorphism types of subspaces of a space X which are obtained by deleting singletons determine X uniquely up to homeomorphism. If the question can be answered affirmatively, such a space is called reconstructible. We prove that in various cases topological properties can be reconstructed. As main result we find that familiar spaces such as the reals '', the rationals '' and the irrationals '' are reconstructible, as well as spaces occurring as Stone-Čech compactifications. Moreover, some non-reconstructible spaces are discovered, amongst them the Cantor set C