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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On subspaces of pseudoradial spaces


Authors: Alan Dow and Jinyuan Zhou
Journal: Proc. Amer. Math. Soc. 127 (1999), 1221-1230
MSC (1991): Primary 54E35
MathSciNet review: 1473663
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Abstract: A topological space $X$ is pseudoradial if each of its non closed subsets $A$ has a sequence (not necessarily with countable length) convergent to outside of $A$. We prove the following results concerning pseudoradial spaces and the spaces $\omega \cup \{p\}$, where $p$ is an ultrafilter on $\omega$:

(i) CH implies that, for every ultrafilter $p$ on $\omega$, $\omega \cup \{p\} $ is a subspace of some regular pseudoradial space.

(ii) There is a model in which, for each P-point $p$, $\omega \cup \{p\}$ cannot be embedded in a regular pseudoradial space while there is a point $q$ such that $\omega\cup\{q\}$ is a subspace of a zero-dimensional Hausdorff pseudoradial space.


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Additional Information

Alan Dow
Affiliation: Department of Mathematics, York University, 4700 Keele Street, North York, Ontario \ Canada M3J 1P3
Email: Alan.Dow@mathstat.yorku.ca

Jinyuan Zhou
Affiliation: Department of Mathematics, York University, 4700 Keele Street, North York, Ontario \ Canada M3J 1P3
Email: jzhou@spicer.com

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04628-6
PII: S 0002-9939(99)04628-6
Keywords: Forcing, CH, ultrafilter, zero-dimensional space, pseudoradial
Received by editor(s): March 17, 1997
Received by editor(s) in revised form: July 30, 1997
Communicated by: Carl Jockusch
Article copyright: © Copyright 1999 American Mathematical Society