- 期刊
A NEW ORDERED COMPACTIFICATION
摘要
A new Wallman-type ordered compactification γ_oX is constructed using maximal CZ-filters (which have filter bases obtained from increasing and decreasing zero sets) as the underlying set. A necessary and sufficient condition is given for γ_oX to coincide with the Nachbin compactification β_o X; in particular γ_oX=β_o X whenever X has the discrete order. The Wallman ordered compactification ω_o X equals γ_oX whenever X is a subspace of R^n. It is shown that γ_oX is always T_1, but can fail to be T_1-ordered or T_2.
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