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)
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer Science+Business Media New York
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-1-4899-0548-2_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-0550-5
Online ISBN: 978-1-4899-0548-2
eBook Packages: Springer Book Archive