Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

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

 

Reflection and weakly collectionwise Hausdorff spaces


Authors: Tim LaBerge and Avner Landver
Journal: Proc. Amer. Math. Soc. 122 (1994), 291-302
MSC: Primary 54D15; Secondary 03E05, 03E35, 03E75
MathSciNet review: 1231038
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that $ \square (\theta )$ implies that there is a first countable $ < \theta $-collectionwise Hausdorff space that is not weakly $ \theta $-collectionwise Hausdorff. We also show that in the model obtained by Levy collapsing a weakly compact (supercompact) cardinal to $ {\omega _2}$, first countable $ {\aleph _1}$-collectionwise Hausdorff spaces are weakly $ {\aleph _2}$-collectionwise Hausdorff (weakly collectionwise Hausdorff). In the last section we show that assuming $ E_\theta ^\omega $, a certain $ \theta $-family of integer-valued functions exists and that in the model obtained by Levy collapsing a supercompact cardinal to $ {\omega _2}$, these families do not exist.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D15, 03E05, 03E35, 03E75

Retrieve articles in all journals with MSC: 54D15, 03E05, 03E35, 03E75


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1231038-X
PII: S 0002-9939(1994)1231038-X
Keywords: Reflection, weakly collectionwise Hausdorff, Levy forcing, Mitchell forcing, fans
Article copyright: © Copyright 1994 American Mathematical Society