Forcing and normality
type: Item
instance of: scholarly article
title: Forcing and normality
zbMATH Open document ID: 0923.54020
DOI: 10.1016/S0166-8641(97)00089-8
author: Renata Grunberg
author: Franklin D. Tall
author: Lucia R. Junqueira
published in: Topology and its Applications
publication date: 1999-10-25T00:00:00Z
review text: In response to questions from the `Open Problems in Topology' book (1990; Zbl 0718.54001), this paper examines the general problem of which standard classes of forcings preserve (non) normality. Some sample results give a good sense of the focus of the many other results. There are examples of normal (and collectionwise normal) spaces for which there is a ccc poset which forces the space to be not normal. It is consistent that there is a non-normal space for which there is a countably closed cardinal preserving forcing which makes the space normal. If adding any number of Cohen reals destroys the normality of a space, the space was a Dowker space. A similar result (in terms of paracompactness) is obtained for adding random reals. If there is a Lusin set, then there is a first countable locally compact normal space such that adding one random real destroys the normality. The final section is a more involved investigation using large cardinals to show it is consistent that adding Cohen reals preserves hereditary normality.
reviewed by: Alan Dow
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 03E40
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 1308015
zbMATH Keywords: normality and forcing
zbMATH Keywords: Cohen real
zbMATH Keywords: pointwise countable type
zbMATH Keywords: reflection
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1308015