Monotone Metacompactness and Related Properties in Scattered Spaces
Keywords:
monotonically metacompact, Noetherian of subinfinite rank, NSR base, NSR pair-base, scatteredAbstract
Monotonically metacompact spaces and related properties are studied in scattered spaces. We show that if a hereditarily metacompact scattered space is monotonically (countably) compact at each point, then the space is monotonically (countably) metacompact. We also show that if a hereditarily metacompact scattered space has a Noetherian (pair-)base of subinfinite rank at each point, then the space has a Noetherian (pair-)base of subinfinite rank. As an application, hereditarily met acompact scattered GO-spaces have a Noetherian base of subinfinite rank, and hence, are monotonically metacompact, improving on a result of Liang-Xue Peng and Li-Jun Wang ["A study on monotonically met acompact and property $(A)((B)), "$ Topology Appl. 245 (2018), 1-20].
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