Linearly stratifiable spaces: some open problems
by
Peter J. Nyikos
University of South Carolina, Columbia, SC 29208

Some remarkably basic questions about linearly stratifiable spaces remain open. For example: (1) does every strongly zero-dimensional linearly stratifiable space have a linearly closure preserving base of clopen sets? (2) and (3): If \alpha is a regular uncountable cardinal, then is every space that is stratifiable over \alpha strongly zero-dimensional? M₂ over \alpha? Both (2) and (3) are unsolved for all regular uncountable \alpha, while (1) is unsolved even for stratifiable spaces. Partial results on these and other open problems will be discussed.

Date received: July 1, 2001