Connected economically metrizable spaces

Taras Banakh, Myroslava Vovk, and Michał Ryszard Wójcik. "Connected economically metrizable spaces." Fundamenta Mathematicae 212.2 (2011): 145-173. <http://eudml.org/doc/283307>.

@article{TarasBanakh2011,
abstract = {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 $d_\{X\}$ of the space X is economical in the sense that for each infinite subspace A ⊂ X the cardinality of the set $\{d_\{X\}(a,b): a,b ∈ A\}$ does not exceed the density of A, $|d_\{X\}(A × A)| ≤ dens(A)$. 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.},
author = {Taras Banakh, Myroslava Vovk, Michał Ryszard Wójcik},
journal = {Fundamenta Mathematicae},
keywords = {non-separably connected complete metric space; economical metric space; quotient map; monotone map},
language = {eng},
number = {2},
pages = {145-173},
title = {Connected economically metrizable spaces},
url = {http://eudml.org/doc/283307},
volume = {212},
year = {2011},
}

TY - JOUR
AU - Taras Banakh
AU - Myroslava Vovk
AU - Michał Ryszard Wójcik
TI - Connected economically metrizable spaces
JO - Fundamenta Mathematicae
PY - 2011
VL - 212
IS - 2
SP - 145
EP - 173
AB - 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 $d_{X}$ of the space X is economical in the sense that for each infinite subspace A ⊂ X the cardinality of the set ${d_{X}(a,b): a,b ∈ A}$ does not exceed the density of A, $|d_{X}(A × A)| ≤ dens(A)$. 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.
LA - eng
KW - non-separably connected complete metric space; economical metric space; quotient map; monotone map
UR - http://eudml.org/doc/283307
ER -