We prove that if there is a model of set-theory which contains no first countable, locally compact, scattered, countably paracompact space , whose Tychonoff square is a Dowker space, then there is an inner model which contains a measurable cardinal.
Arhangel’skii proved that if a first countable Hausdorff space is Lindelöf, then its cardinality is at most . Such a clean upper bound for Lindelöf spaces in the larger class of spaces whose points are has been more elusive. In this paper we continue the agenda started by the second author, [Topology Appl. 63 (1995)], of considering the cardinality problem for spaces satisfying stronger versions of the Lindelöf property. Infinite games and selection principles, especially the Rothberger property,...
We work towards establishing that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. At a crucial step we use some still unpublished results announced by Todorcevic. Modulo this and the large cardinal, this answers a question of S. Watson. Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space...