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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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