# A Note on Monotonically Metacompact Spaces - Mathematics > General Topology

A Note on Monotonically Metacompact Spaces - Mathematics > General Topology - Download this document for free, or read online. Document in PDF available to download.

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/