Nowhere dense choices and π-weight
Abstract
The paper is devoted to inequalities between π0(X) and πd(X) where
π0(X) := min{π(U): U open and non-empty subset of X},
πd(X) := min{|𝓑|: every open and dense subset of X containes an element from 𝓑}.
From these definitions πd(X) ≤ π0(X) for every space X. In the paper we construct a space X for which πd(X)=ω1 and π0(X)=2ℵ0.
References
1. J. Berwise, Handbook of Mathematical Logic, North Holland, 1977.
2. E. van Douwen, F. Tall, W. Weiss, Non-metrizable hereditarily Lindelöf spaces with point-countable bases from CH, Proc. Amer. Math. Soc. 64 (1977), 139-145.
3. R. Engelking, General Topology, Polish Scientific Publishers, Warsaw, 1977.
4. A. Hajnal, I. Juhász, On hereditarily α-Lindelöf and hereditarily α-separable spaces II, Fund. Math. 81 (1974), 147-158.
5. I. Juhász, Cardinal Functions - Ten Years Later, Mathematical Centre, Amsterdam, 1980.
6. F.D. Tall, Some applications of a generalized Martin's Axiom, Trans. Amer. Math. Soc. (to appear).
2. E. van Douwen, F. Tall, W. Weiss, Non-metrizable hereditarily Lindelöf spaces with point-countable bases from CH, Proc. Amer. Math. Soc. 64 (1977), 139-145.
3. R. Engelking, General Topology, Polish Scientific Publishers, Warsaw, 1977.
4. A. Hajnal, I. Juhász, On hereditarily α-Lindelöf and hereditarily α-separable spaces II, Fund. Math. 81 (1974), 147-158.
5. I. Juhász, Cardinal Functions - Ten Years Later, Mathematical Centre, Amsterdam, 1980.
6. F.D. Tall, Some applications of a generalized Martin's Axiom, Trans. Amer. Math. Soc. (to appear).
JuhászI., & WeissW. A. R. (1986). Nowhere dense choices and π-weight. Annales Mathematicae Silesianae, 2, 85-91. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14327
Istvan Juhász
Institute of Mathematics, Hungarian Academy of Science Hungary
Institute of Mathematics, Hungarian Academy of Science Hungary
William A. R. Weiss
Department of Mathematics, University of Toronto, Canada Canada
Department of Mathematics, University of Toronto, Canada Canada
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