Connected economically metrizable spaces

• Autorzy: Taras Banakh , Myroslava Vovk , Michał Ryszard Wójcik
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54G15: Pathological spaces
• 54E35: Metric spaces, metrizability
• 54F15: Continua and generalizations
• 54C30: Real-valued functions
• 54G20: Counterexamples
• 54B30: Categorical methods
• 54E50: Complete metric spaces
• 54D05: Connected and locally connected spaces (general aspects)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 212
• Numer: 2
• Strony: 145-173

Daty

wydano

2011

Twórcy

autor

Taras Banakh

• Instytut Matematyki, Uniwersytet Humanistyczno-Przyrodniczy, Jana Kochanowskiego, Kielce, Poland
• Department of Mathematics, Ivan Franko National University of Lviv, Universytetska 1, 79000, Lviv, Ukraine

autor

Myroslava Vovk

• National University, Lvivska Politechnika, Lviv, Ukraine

autor

Michał Ryszard Wójcik

• Department of Mathematics, University of Louisville, Louisville, KY, U.S.A.
• Institute of Geography and Regional Development, University of Wrocław, 50-137 Wrocław, Poland

Identyfikatory

DOI

10.4064/fm212-2-3