Infinite Products of Weakly -Refinable Normal Spaces

This paper mainly proves following : (1) Let X=∏ σ∈ X σ be ||-paracompact,X is normal weak θ-refinable iff ∏ σ∈ X σ is normal weak θ-refinable for every F∈|| ω .(2)Let X=∏ i∈ω X i is countable paracompact, then the following are equivalent:X is normal weak θ-refinable;F∈ ω ,∏ σ∈F X σ is normal weak θ-refinable;n∈ω,∏ i≤n X i is normal weak θ-refinable.