This paper first prove an inverse limit theorem of strongly submetacompact spaces; By using this, two Tychonoff product theorems of infinit factor spaces are obtained; Finally, it is proved that the equalentness on strongly submetacompact spaces and submetacompact spaces is proved.

Nearly submetacompact spaces and nearly strongly submetacompact spaces;

We define the nearly submetacompact space and give a characterization of it.