Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T22:59:05.972Z Has data issue: false hasContentIssue false
  • English
  • Français

On Compact Separable Radial Spaces

Published online by Cambridge University Press:  20 November 2018

Alan Dow
Alan Dow*
Affiliation:
4700 Keele Street Mathematics and Statistics York University York, Ontario M3J 1P3
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.

If A and B are disjoint ideals on ω, there is a tower preserving σ-centered forcing which introduces a subset of ω which meets every infinite member of A in an infinite set and is almost disjoint fromeverymember of B. We can then produce a model in which all compact separable radial spaces are Fréchet, thus answering a question of P. Nyikos. The question of the existence of compact ccc radial spaces which are not Fréchet was first asked by Chertanov (see [Arh78]).

Keywords

54D30separableFrechétradial
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 4 , 01 December 1997 , pp. 422 - 432
Copyright
Copyright © Canadian Mathematical Society 1997

References

[Arh78] Arhangel’skii, A.V., Structure and classification of topological spaces and cardinal invariants,Uspekhi Mat. Nauk (1978), 29–84.Google Scholar
[BD85] Baumgartner, J. and Dordal, P., Adjoining dominating functions, J. Symbolic Logic 50 (1985), 94–101.Google Scholar
[Bel81] Bell, M. G., On the combinatorial principle p(c), Fund. Math. 114 (1981), 149–157.Google Scholar
[JS92] Juhász, I. and Szentmiklóssy, Z., On convergent free sequences in compact spaces, Proc. Amer. Math. Soc. (4) 116 (1992), 1153–1160.Google Scholar