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A Note on Monotonically Metacompact Spaces

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

General Topology · Submitted 21 Oct 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that any metacompact Moore space is monotonically metacompact and use that result to characterize monotone metacompactness in certain generalized ordered (GO)spaces.

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arXiv ID0910.4106 (version 1)
Pith ID2BDM6J5X, Pith's permanent record of this paper and its review
CitationDavid J. Lutzer, Harold R. Bennett, Klaas Pieter Hart. "A Note on Monotonically Metacompact Spaces." arXiv:0910.4106 (2009). https://pith.science/paper/2BDM6J5X
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,908 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.45 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We show that any metacompact Moore space is monotonically metacompact and use that result to characterize monotone metacompactness in certain generalized ordered (GO)spaces. We show, for example, that a generalized ordered space with a sigma-closed-discrete dense subset is metrizable if and only if it is monotonically (countably) metacompact, that a monotonically (countably) metacompact GO-space is hereditarily paracompact, and that a locally countably compact GO-space is metrizable if and only if it is monotonically (countably) metacompact. We give an example of a non-metrizable LOTS that is monotonically metacompact, thereby answering a question posed by S. G. Popvassilev. We also give consistent examples showing that if there is a Souslin line, then there is one Souslin line that is monotonically countable metacompact, and another Souslin line that is not monotonically countably metacompact.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show that any metacompact Moore space is monotonically metacompact and use that result to characterize monotone metacompactness in certain generalized ordered (GO)spaces. contribution 0.58 0.96 0.68 asserted 1.00
s1 We show, for example, that a generalized ordered space with a sigma-closed-discrete dense subset is metrizable if and only if it is monotonically (countably) metacompact, that a monotonically (countably) metacompact GO-space is hereditarily paracompact, and that a locally countably compact GO-space is metrizable if and only if it is monotonically (countably) metacompact. result 0.98 0.94 0.25 asserted 1.00
s2 We give an example of a non-metrizable LOTS that is monotonically metacompact, thereby answering a question posed by S. G. Popvassilev. result 0.59 0.97 0.14 asserted 1.00
s3 We also give consistent examples showing that if there is a Souslin line, then there is one Souslin line that is monotonically countable metacompact, and another Souslin line that is not monotonically countably metacompact. result 0.73 0.93 0.07 asserted 0.52

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We show that any metacompact Moore space is monotonically metacompact and use that result to characterize monotone metacompactness in certain generalized ordered (GO)spaces. We show, for example, that a generalized ordered space with a sigma-closed-discrete dense subset is metrizable if and only if it is monotonically (countably) metacompact, that a monotonically (countably) metacompact GO-space is hereditarily paracompact, and that a locally countably compact GO-space is metrizable if and only if it is monotonically (countably) metacompact. We give an example of a non-metrizable LOTS that is monotonically metacompact, thereby answering a question posed by S. G. Popvassilev. We also give consistent examples showing that if there is a Souslin line, then there is one Souslin line that is monotonically countable metacompact, and another Souslin line that is not monotonically countably metacompact.

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