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://www.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
The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.
- License
This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license. - Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s. - User Rights
Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor. - Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
