几乎强次亚紧空间的无限乘积性质

The Tychonoff Prdouct Properity of Nearly Strong Submetacompact Spaces

对几乎强次亚紧空间进行了研究,获得了无限个因子的乘积的2个等价定理:①如果X=∏τ∈∑Xτ是|λ|-仿紧空间,则X是几乎强次亚紧空间当且仅当F∈[∑]<ω,X=∏τ∈FXτ是几乎强次亚紧空间。②设X=∏i∈ωXi是可数仿紧的,则下列3条等价:X是几乎强次亚紧的;F∈[ω]<ω,X=∏i∈FXi是几乎强次亚紧的;存在nx∈ω,使得n≥nx,∏i≤nXi是几乎强次亚紧的。

The following is proved: ①Let X=∏τ∈∑Xτ be paracompact,then X is nearly strong submetacompact space for every F∈[∑]<ω,then X=∏r∈FXτ is nearly strong submetacompact space.②Let X=∏i∈ωXi be countable paracompact,then the following is equivalent: X is nearly strong submetacompact;for every F∈[ω]<ω,X=∏i∈FXi is nearly strong submetacompact;existing nx∈ω,such that for every n≥nx,∏i≤nXi is nearly strong submetacompact.