A note on paracompactness in generalized ordered spaces

Abstract:

In this paper, 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 $\{G(x)\colon x\in X\}$ of open sets in $X$ satisfying $x\in G(x)$ for each $x$, there is a closed discrete subset $D$ of $X$ satisfying $X=\bigcup \{G(x)\colon x\in D\}$.