Abstract
In this paper we consider topological variants of Zermelo’s well-ordering theorem. Given topological notions, P, Q of the form “some class of subsets of a space X is wellorderable”, we consider assertions of the form “if a space X satisfies P, also Q holds for X”. The properties to be considered here are related to the following cardinal invariants: cardinality of the topology, weight, density, Lindelöf-degree, spread, (hereditary) cellularity. Accordingly we define for a topological space (X, X)
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References
Brunner, N., 1982a, Dedekind-Endlichkeit und Wohlordenbarkeit, Mh. Math., 94:9–31.
Brunner, N., 1982b, Geordnete Läuchli Kontinuen, Fund. Math., 116:67–73.
Brunner, N., 1983, The Axiom of Choice in Topology, Notre Dame J. F. L., 24:305–317.
Brunner, N., 1984, Hewitt Spaces, Math. Balkanica (to appear).
Jech, T., 1968, Bemerkungen zum Auswahlaxiom, Casopis pest, mat., 93:30–31.
Jech, T., 1973, “The Axiom of Choice,” North-Holland, Amsterdam.
Rubin, H. and Rubin, J. E., 1985, Equivalents of the Axiom of Choice II, in: “Studies in Logic,” North Holland, (to appear).
Steen, L. A. and Seebach, J. A., 1978, “Counterexamples in Topology,” Springer, New York.
Solovay, R., 1970, A Model of Set Theory in which every Set of Reals is Lebesgue Measurable, Ann. Math., 92:1–56.
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Brunner, N. (1985). Wellordering Theorems in Topology. In: Dorn, G., Weingartner, P. (eds) Foundations of Logic and Linguistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0548-2_12
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DOI: https://doi.org/10.1007/978-1-4899-0548-2_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-0550-5
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