亚紧空间和σ-亚紧空间的无限乘积

Nearly orthocompact spaces

主要证明了如下结果 :用P表示下列诸覆盖性质之一 :亚紧 ;次亚紧 ;弱次亚紧 ;σ -亚紧 .( 1)如果X =∏α∈ΛXα 是 |Λ| -仿紧空间 ,则X具有P当且仅当 F∈ [Λ]<ω,∏α∈FXα 具有P ;( 2 )如果X =∏i∈ωXi 是可数仿紧的 ,则下列三条等价 :X具有P : F∈ [ω]<ω,∏i∈FXi具有P : n <ω ,∏i≤nXi,具有P .

This paper mainly proves following: (1) Let X=∏α∈ΛX α be|Λ| - paracompact, X is nearly orthocompact if ∏α∈FX α is nearly orthocompact for every F∈ <ω(2) Let X=∏i∈ω X i be countable paracompact,then the following are equivalent: X is nearly orthocompact for everyF∈ <ω ;F∈ <ω ∏i∈FX i , is nearly orthocompact;n∈ω,∏inX i is nearly orthocompact. Finally, we also obtain equalent propositions on nea rly orthocompact.