On monotone paracompactness

Popvassilev, Strashimir G.; Porter, John E.

doi:10.1016/j.topol.2014.03.001

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…It is well-known that metacompact GO-spaces (and more generally metacompact collectionwise normal spaces) are paracompact [5,Theorem 5.3.3]. A monotone version of this result holds for GO-spaces, and partially answers our Question 2.6(b) in [14].…”

Section: Monotone Operators In Go-spacesmentioning

confidence: 57%

“…The following is a variation of our Question 2.6(d) in [14] (where "monotone locally-finite operator" meant "monotone open locally-finite operator").…”

Section: Monotone Operators In Go-spacesmentioning

confidence: 99%

“…Question 2.11. Does every LOTS X with a monotone locally-finite (open) operator have a Nötherianly locally-finite base (as defined in [14])?…”

Section: Monotone Operators In Go-spacesmentioning

confidence: 99%

“…In [15], Stares showed that different characterizations of paracompact spaces, when monotonized, may give rise to different classes of spaces, and asked which monotonized characterizations coincide. The authors showed in [14] that the class of spaces with a monotone open locally-finite operator is strictly larger than the class of protometrizable spaces.…”

Section: Introductionmentioning

confidence: 99%

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Monotone Covering Properties defined by Closure-Preserving Operators

Popvassilev¹,

Porter²

2017

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We continue Gartside, Moody, and Stares' study of versions of monotone paracompactness. We show that the class of spaces with a monotone closure-preserving open operator is strictly larger than those with a monotone open locally-finite operator. We prove that monotonically metacompact GO-spaces have a monotone open locally-finite operator, and so do GO-spaces with a monotone (open or not) closure-preserving operator, whose underlying LOTS has a σ-closed-discrete dense subset. A GO-space with a σ-closeddiscrete dense subset and a monotone closure-preserving operator is metrizable. A compact LOTS with a monotone open closure-preserving operator is metrizable.Dedicated to our mentor and dear friend Gary Gruenhage with gratitude and well-wishes on the occasion of his 70-th birthday.

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Section: Monotone Operators In Go-spacesmentioning

confidence: 57%

“…The following is a variation of our Question 2.6(d) in [14] (where "monotone locally-finite operator" meant "monotone open locally-finite operator").…”

Section: Monotone Operators In Go-spacesmentioning

confidence: 99%

“…Question 2.11. Does every LOTS X with a monotone locally-finite (open) operator have a Nötherianly locally-finite base (as defined in [14])?…”

Section: Monotone Operators In Go-spacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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