Forcing and normality
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.
scientific article; zbMATH DE number 1308015
scientific article