A TOPOLOGICAL VARIATION OF THE RECONSTRUCTION CONJECTURE

Abstract

AbstractThis 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 ℝ, the rationals ℚ and the irrationals ℙ are reconstructible, as well as spaces occurring as Stone–Čech compactifications. Moreover, some non-reconstructible spaces are discovered, amongst them the Cantor set C.