2015/09/24 by Paul Gartside, Gartside, Paul, Max F. Pitz +3
Mathematics · #54D05 #54D35 #54E45 #54F15 #Combinatorics (math.CO) #FOS: Mathematics #General Topology (math.GN) #Primary 05C60 #Secondary 54B05 #math.CO #math.GN #msc:05C60 #msc:54B05 #msc:54D05 #msc:54D35 #msc:54E45 #msc:54F15
paper · pdf · doi:10.48550/arxiv.1509.07769
13 pages
arxiv created 2015/09/24 · arxiv updated 2015/09/28
The deck of a topological space X is the set D(X)=\[X ∖ \x\] \colon x ∈ X\, where [Z] denotes the homeomorphism class of Z. A space X is topologically reconstructible if whenever D(X)=D(Y) then X is homeomorphic to Y. It is shown that all metrizable compact connected spaces are reconstructible. It follows that all finite graphs, when viewed as a 1-dimensional cell-complex, are reconstructible in the topological sense, and more generally, that all compact graph-like spaces are reconstructible.