2013/11/29 by Max Pitz, Max F. Pitz, Pitz, Max F. +2
Computer Science · Mathematics · #54A05 #54B05 #54Dxx #54E35 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Primary 54B99 #Secondary 05C60 #Topological and Geometric Data Analysis #math.GN #msc:05C60 #msc:54A05 #msc:54B05 #msc:54B99 #msc:54Dxx #msc:54E35
paper · pdf · doi:10.48550/arxiv.1311.7625
14 pages
arxiv created 2013/11/29 · openalex publication_date 2013/11/29 · arxiv updated 2013/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℝ, the rationals ℚ and the irrationals P are reconstructible, as well as spaces occurring as Stone-Cech compactifications. Moreover, some non-reconstructible spaces are discovered, amongst them the Cantor set C.