正规弱θ空间的无限Tychonoff积

Tychonoff Products of Weakly θ-Refinable Spaces

中文关键词:  弱-θ可加  正规  |Σ|-仿紧  可数仿紧

英文关键词:θ-refinable  normal  |∑| -paracompact  countable paracompact.

中文摘要:

      本文证明:(1)如果X=∏_σ∈∑X_σ是|∑|-仿紧空间,则X是正规弱θ可加空间当且仅当?F∈[∑]^<ω,∏_σ∈FX_σ是正规弱θ-可加空间.(2)设X=∏_i∈ωX_i是可效仿紧的,则下列三条等价:是正规弱θ-可加的;?F∈[ω]^<ω,∏_i∈FX_i是正规弱θ-可加的;?n∈ω;∏_i≤n

英文摘要:

      This paper obtains the following conclusions: (1) Let X=∏_σ∈∑X_σ be |∑|-para-compact, then it is normal weak θ-refinable iff ∏_σ∈FX_σ is normal weakθ-refinable for every F∈[∑]^<ω.(2) For countable paracompact X =∏_i∈ωX_i, the followings are equivalent; X is normal weak θ-refinable;?F∈[∑]^<ω,∏_σ∈FX_σ is normal weakθ-refinable; ?n∈ω;∏_i≤nX_i is normal weak θ-refinable.