Tychonoff Products of Weakly θ-Refinable Spaces

Abstract:

      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.