Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T14:35:54.722Z Has data issue: false hasContentIssue false
  • English
  • Français

Orders of π-Bases

Published online by Cambridge University Press:  20 November 2018

Isaac Gorelic
Isaac Gorelic*
Affiliation:
Government of Canada, Ottawa, ON e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We extend the scope of B. Shapirovskii's results on the order of $\pi $-bases in compact spaces and answer some questions of V. Tkachuk.

Keywords

54A2503E1003E7554A35Shapirovskii π-basepoint-countable π-basefree sequencescanonical form for ordinals
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 2 , 01 June 2010 , pp. 286 - 294
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] Alexandroff, P. S. and Urysohn, P. S., Mémoire sur les espaces topologiques compacts. Verhan-Delingen der Koninklijke Akademie van Wetenschappen te Amsterdam, 14(1929), 1–96.Google Scholar
[2] Engelking, R., General Topology, Heldermann Verlag, Berlin 1989.Google Scholar
[3] Kunen, K., Set Theory, An Introduction to Independence Proofs. Studies in Logic and the Foundations of Mathematics 102. North-Holland Publishing, Amsterdam, 1980.Google Scholar
[4] Magidor, M., On the singular cardinals problem. I. Israel J. Math. 28(1977), no. 1-2, 1–31. doi:10.1007/BF02759779Google Scholar
[5] Shapirovskii, B. E., Discrete subspaces of topological spaces. Weight, tightness and Suslin number. Dokl. Akad. Nauk SSSR 202(1972), 779–782.Google Scholar
[6] Shapirovskii, B. E., Mappings on Tikhonov Cubes. (Russian) Uspekhi Mat. Nauk 35(1980), no. 3, 122–130.Google Scholar
[7] Shapirovskii, B. E., Cardinal invariants in compacta. (Russian) In: Seminar on General Topology. Moskov. Gos. Univ., Moscow, 1981, pp. 162–187.Google Scholar
[8] Tkachuk, V. V., Point-countable π-bases in first-countable and similar spaces. Fund. Math. 186(2005), no. 1, 55–69. doi:10.4064/fm186-1-4Google Scholar
[9] Todorčević, S., Remarks on cellularity in products. Compositio Math. 57(1986), no. 3, 357–372.Google Scholar
[10] Todorčević, S., Free sequences. Topology Appl. 35(1990), no. 2-3, 235–238. doi:10.1016/0166-8641(90)90108-EGoogle Scholar
[11] Todorčević, S., Some applications of S and L combinatorics. In: The Work of Mary Ellen Rudin. Ann. New York Acad. Sci. 705. New York Acad. Sci., New York, 1993, pp. 130–167.Google Scholar