中文摘要：

主要证明如下结论：设X=lim←{Xα,παβ,Λ},λ=｜Λ｜并且每个投射πα是开满映射,如果X是λ-仿紧的且每个Xα是序列中紧的,则X是序列中紧的;如果X是遗传λ-仿紧的且每个Xα是遗传序列中紧的,则X是遗传序列中紧的.

英文摘要：

This paper proves the following results.Let X=lim←{Xα,παβ,Λ},λ=｜Λ｜ and each projection πa is an openand onto mapping, if X is λ-paracompact and each Xa is sequentially mesocompact spaces, then X is sequentially mesocompact spaces, if X is hereditarily ,λ-paracompact and each Xa is hereditarily sequentially mesocompact spaces, then X is hereditarily sequentially mesocompact spaces.