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A topological property $$\mathscr {P}$$ P is reflected in continuous images of weight at most $$\omega _1$$ ω 1 if a space X has $$\mathscr {P}$$ P whenever every continuous image of X of weight at most $$\omega _1$$ ω 1 has $$\mathscr {P}$$ P . When X is a generalized ordered space, we consider a number of topological properties including feeble Lindelöfness...
In this paper we examine the interactions between the topology of certain linearly ordered topological spaces (LOTS) and the properties of trees in whose branch spaces they embed. As one example of the interaction between ordered spaces and trees, we characterize hereditary ultraparacompactness in a LOTS (or GO-space) X in terms of the possibility of embedding the space X in the branch space of a...
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