Geodesic
A TOPOLOGICAL VARIATION OF THE RECONSTRUCTION CONJECTURE
Glasgow mathematical journal, Tome 59 (2017) no. 1, pp. 221-235

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DOI

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–Čech compactifications. Moreover, some non-reconstructible spaces are discovered, amongst them the Cantor set C. 
PITZ, MAX F.; SUABEDISSEN, ROLF. A TOPOLOGICAL VARIATION OF THE RECONSTRUCTION CONJECTURE. Glasgow mathematical journal, Tome 59 (2017) no. 1, pp. 221-235. doi: 10.1017/S0017089516000124
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     title = {A {TOPOLOGICAL} {VARIATION} {OF} {THE} {RECONSTRUCTION} {CONJECTURE}},
     journal = {Glasgow mathematical journal},
     pages = {221--235},
     year = {2017},
     volume = {59},
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     doi = {10.1017/S0017089516000124},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000124/}
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