A topological space is non-separably 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 non-separably connected complete metric space X under a monotone quotient map. The metric of the space X is economical in the sense that for each infinite subspace A ⊂ X the cardinality of the set does not exceed the density of A, . The construction of the space X determines a functor : Top → Metr from the category Top of topological spaces and their continuous maps into the category Metr of metric spaces and their non-expanding maps.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-2-3,
author = {Taras Banakh and Myroslava Vovk and Micha\l\ Ryszard W\'ojcik},
title = {Connected economically metrizable spaces},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {145-173},
zbl = {1252.54021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-2-3}
}
Taras Banakh; Myroslava Vovk; Michał Ryszard Wójcik. Connected economically metrizable spaces. Fundamenta Mathematicae, Tome 215 (2011) pp. 145-173. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-2-3/