Connected economically metrizable spaces
General Topology
2011-10-11 v4 Metric Geometry
Abstract
A topological space is nonseparably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image of a nonseparably connected complete metric space Eco(X) under a monotone quotient map. The metric d of the space Eco(X) is economical in the sense that for each infinite subspace A of X the cardinality of the set {d(a,b):a,b in A} does not exceed the density of A. The construction of the space Eco(X) determines a functor Eco from the category Top of topological spaces and their continuous maps into the category Metr of metric spaces and their non-expanding maps.
Cite
@article{arxiv.0901.0236,
title = {Connected economically metrizable spaces},
author = {T. Banakh and M. Vovk and M. R. Wójcik},
journal= {arXiv preprint arXiv:0901.0236},
year = {2011}
}
Comments
20 pages