Tychonoff Products of Weakly Subortho-compact Spaces
JI Guang-yue
Abstract
JI Guang-yue
Abstract
The following conclusions are proved:(1) Let X= Πσ ∈ΣXσbe │Σ│-paracompact,then it is weakly subortho-compact if Πσ∈FXσis weakly subortho-compact for every F∈[Σ] ω.(2) For countable paracompact X=∏i∈ωXi,the followings are equivalent:X is weakly subortho-compact,F∈[ω] ω,∏i∈FXi is weakly subortho-compact;n∈ω,∏i≤nXi is subortho-compact.
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The following conclusions are proved:(1) Let X= Πσ ∈ΣXσbe │Σ│-paracompact,then it is weakly subortho-compact if Πσ∈FXσis weakly subortho-compact for every F∈[Σ] ω.(2) For countable paracompact X=∏i∈ωXi,the followings are equivalent:X is weakly subortho-compact,F∈[ω] ω,∏i∈FXi is weakly subortho-compact;n∈ω,∏i≤nXi is subortho-compact.
Key concepts: Paracompact space, Tychonoff space, Countable set, Locally compact space, Mathematics, Compact space, Pure mathematics, Relatively compact subspace