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A note on paracompactness in generalized ordered spaces. (English) Zbl 0885.54023
Summary: We show that for generalized ordered spaces, paracompactness is equivalent to Property D, where a space $$X$$ is said to have Property D if, given any collection $$\{G(x): x\in X\}$$ of open sets in $$X$$ satisfying $$x\in G(x)$$ for each $$x$$, there is a closed discrete subset $$D$$ of $$X$$ satisfying $$X=\bigcup \{G(x): x\in D\}$$.

##### MSC:
 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
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##### References:
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