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Abstract: We show that any metacompact Moore space is monotonically metacompact and usethat result to characterize monotone metacompactness in certain generalizedordered GOspaces. We show, for example, that a generalized ordered space witha sigma-closed-discrete dense subset is metrizable if and only if it ismonotonically countably metacompact, that a monotonically countablymetacompact GO-space is hereditarily paracompact, and that a locally countablycompact GO-space is metrizable if and only if it is monotonically countablymetacompact. We give an example of a non-metrizable LOTS that is monotonicallymetacompact, thereby answering a question posed by S. G. Popvassilev. We alsogive consistent examples showing that if there is a Souslin line, then there isone Souslin line that is monotonically countable metacompact, and anotherSouslin line that is not monotonically countably metacompact.



Author: Harold R. Bennett, Klaas Pieter Hart, David J. Lutzer

Source: https://arxiv.org/



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