Abstract:

 It is proved that the  space X is a submesocompact space if and only if every scattered patition of X has a θ-cf-open expansions. If every scattered patition of X has a θcfopen expansions, than X is a hereditarily submesocompact space, but not established and given example. One result of submesocompact space is given.

Key words: submesocompactness; hereditarily submesocompactness; scattered patition; θ-cf-expandability