Inverse Limits of Strong Submetacompactness

In this paper,first obtained is an inverse limit theorem of strong submetacompact spaces if X = lim ←{ X σ,π σ ρ, }and every π σ is of full mapping;if X is |  |- paracompact and every X α is submetacompact, X is strongly submetacompact.Based on the inverselimit theorem,two Tychonoff infinite product theorems in the strong submetacompact spaces are deduccd:if X = α∈A X α is| A |- paracompact space, X is strong submetacompact space ,when σ ∈  , α ∈ σ X α is strong submetacompact space,among which  = ω .