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Connected economically metrizable spaces

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Banakh T., Vovk M., Wójcik M.

Fundamenta Mathematicae

2011

tom 212

nr 2

145-173

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 𝓔X under a monotone quotient map. The metric $d_{𝓔X}$ of the space 𝓔X is economical in the sense that for each infinite subspace A ⊂ X the cardinality of the set ${d_{𝓔X}(a,b): a,b ∈ A}$ does not exceed the density of A, $|d_{𝓔X}(A × A)| ≤ dens(A)$. The construction of the space 𝓔X determines a functor 𝓔: 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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Banakh T.

1 Vovk M.

1 Wójcik M.

1 2011

Wyniki wyszukiwania

Connected economically metrizable spaces