关于σ-meso紧空间的无限乘积

Product Properties on σ-Mesocompact Spaces

证明了σ -meso紧空间乘积的两个主要结果 :(1)若X =Xσ∈ Xσ 是 | |-仿紧的 ,则X是σ -meso紧的当且仅当 F∈ [ ]<ω,∏σ∈F是Xσ 是σ -meso紧的 ;(2 )设X=∏i∈ωXi,则下列各条等价 :①X是遗传σ -meso紧的 ;② σ∈ [ω]<ω,∏i∈σXi 是遗传σ -meso紧的 ;③ n∈ω∏i<n,Xi 是遗传σ -meso紧的 .

This paper mainly proves the following two results: (1)Let X=∏ σ< X σ be a|| -paracompact space,then X is σ-mesocompact iff ∏ σ<F X σ is σ-mesocompact for every F∈ <ω ,(2)Let X=∏ i<ω X i , then the following are equivalent: ①X is hereditarily σ-mesocompact ;②∏ i<δ X i is hereditarily σ-mesocompact for every σ∈ <ω ;③∏ i<n X i is hereditarily σ-mesocompact for every n∈ω.