On subspaces of pseudoradial spaces
Authors:
Alan Dow and Jinyuan Zhou
Journal:
Proc. Amer. Math. Soc. 127 (1999), 12211230
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 Ppoint , cannot be embedded in a regular pseudoradial space while there is a point such that is a subspace of a zerodimensional 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/S0002993999046286
PII:
S 00029939(99)046286
Keywords:
Forcing,
CH,
ultrafilter,
zerodimensional 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
