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A topology on the union of the double arrow space and the integers. (English) Zbl 0632.54023
We construct a topology on the union of the double arrow space (Cantor set version) and the integers which is a hereditarily Lindelöf hereditarily separable 0-dimensional compact Hausdorff space but not the continuous image of a closed subspace of the product of the double arrow space and the closed unit interval (answering a question of Fremlin).

54G20 Counterexamples in general topology
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54D30 Compactness
54C05 Continuous maps
Full Text: DOI
[1] Filippov, V., On perfectly normal bicompacta, Soviet math. doklady, 10, 1505-1507, (1969) · Zbl 0198.55502
[2] D.H. Fremlin, Consequences of Martin’s Axiom, Question List, Preprint. · Zbl 1156.03050
[3] Hodel, R., Cardinal function I handbook of set theoretic topology, (), 1-61
[4] Engelking, R., General topology, (1977), Polish Scientific Publishing Warszawa
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