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Abstract: A topological space is nonseparably connected if it is connected but all ofits connected separable subspaces are singletons. We show that each connectedsequential topological space X is the image of a nonseparably connectedcomplete metric space EcoX under a monotone quotient map. The metric d of thespace EcoX is economical in the sense that for each infinite subspace A of Xthe cardinality of the set {da,b:a,b in A} does not exceed the density of A.The construction of the space EcoX determines a functor Eco from the categoryTop of topological spaces and their continuous maps into the category Metr ofmetric spaces and their non-expanding maps.



Autor: T. Banakh, M. Vovk, M. R. Wójcik

Fuente: https://arxiv.org/







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