Linearly Singly Bi-k-spaces
The cardinal functions of pseudocharacter, closed pseudocharacter, and character are used to examine H-closed spaces and to contrast the differences between H-closed and minimal Hausdorff spaces. An H-closed space is produced with the properties that and .
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 At a crucial step we use some still unpublished results announced by Todorcevic.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 Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space...