Abstract
We prove that the one-point Lindelöfication of a discrete space of cardinality ω 1 is homeomorphic to a subspace of C p (X) for some hereditarily Lindelöf space X if the axiom
holds.
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References
Arhangel’skii A.V., Some problems and lines of investigation in general topology, Comment. Math. Univ. Carolin., 1988, 29(4), 611–629
Arhangel’skii A.V., Problems in C p-theory, In: Open Problems in Topology, North-Holland, Amsterdam-New York-Oxford-Tokyo, 1990, 601–616
Arhangel’skii A.V., Topological Function Spaces, Math. Appl. (Soviet Ser.), 78, Kluwer, Dordrecht-Boston-London, 1992
Arhangel’skii A.V., Uspenskii V.V., On the cardinality of Lindelöf subspaces of function spaces, Comment. Math. Univ. Carolin., 1986, 27(4), 673–676
Engelking R., General Topology, 2nd ed., Sigma Ser. Pure Math., 6, Heldermann, Berlin, 1989
Fremlin D.H., Consequences of Martin’s Axiom, Cambridge Tracts in Math., 84, Cambridge University Press, Cambridge, 1984
Fuchino S., Shelah S., Soukup L., Sticks and clubs, Ann. Pure Appl. Logic, 1997, 90(1–3), 57–77
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Okunev, O. The one-point Lindelöfication of an uncountable discrete space can be surlindelöf. centr.eur.j.math. 11, 1750–1754 (2013). https://doi.org/10.2478/s11533-013-0279-8
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DOI: https://doi.org/10.2478/s11533-013-0279-8
axiom