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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).

MSC:
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
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References:
[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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