2016/04/26 by Тарас Банах, Taras Banakh, Bogdan Bokalo +1 · 1 citation
Decision Sciences · Mathematics · #Advanced Topology and Set Theory #Bijection #Combinatorics #Dimension (graph theory) #Discrete mathematics #Fuzzy and Soft Set Theory #Homeomorphism (graph theory) #Mathematical analysis #Mathematics #Metrization theorem #Omega #Physics #Rings, Modules, and Algebras #Separable space #Space (punctuation) #Subspace topology #Topological conjugacy #Topological space #Topology (electrical circuits) #math.GN #msc:54A25 #msc:54C08 #msc:54F65
paper · pdf · doi:10.1016/j.topol.2017.02.036
published in Topology and its Applications 221, 91-106 (Elsevier BV) · 16 pages
arxiv created 2016/04/26 · openalex created_date 2016/06/24 · openalex publication_date 2017/02/11 · arxiv updated 2017/06/21 · openalex updated_date 2026/08/05
A map f:X→ Y between topological spaces is called weakly discontinuous if each subspace A⊂ X contains an open dense subspace U⊂ A such that the restriction f|U is continuous. A bijective map f:X→ Y between topological spaces is called a weak homeomorphism if f and f-1 are weakly discontinuous. We study properties of topological spaces preserved by weakly discontinuous maps and weak homeomorphisms. In particular, we show that weak homeomorphisms preserve network weight, hereditary Lindelöf number, dimension. Also we classify infinite zero-dimensional σ-Polish metrizable spaces up to a weak homeomorphism and prove that any such space X is weakly homeomorphic to one of 9 spaces: ω, 2ω, \mathbb Nω, \mathbb Q, \mathbb Q⊕ 2ω, \mathbb Q× 2ω, \mathbb Q⊕\mathbb Nω, (\mathbb Q× 2ω)⊕\mathbb Nω, \mathbb Q×\mathbb Nω.