Star covering properties in pseudocompact spaces

In this paper, we construct the following three examples:(1)There exists a pseudocompact Tychonoff space that is not star Lindelöf;(2)There exists a pseudocompact star σ-compact Tychonoff space that is not star countable;(3)There exists a star Lindelöf Moore space (hence first countable) that is not star Lindelöf.