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 is pseudoradial if each of its non closed subsets has a sequence (not necessarily with countable length) convergent to outside of . We prove the following results concerning pseudoradial spaces and the spaces , where is an ultrafilter on :

(i) CH implies that, for every ultrafilter on , is a subspace of some regular pseudoradial space.

(ii) There is a model in which, for each P-point , cannot be embedded in a regular pseudoradial space while there is a point such that 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

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