Antidiamond principles and topological applications

Eisworth, Todd; Nyikos, Peter

doi:10.1090/s0002-9947-09-04705-9

Cited by 13 publications

(19 citation statements)

References 35 publications

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“…Proof. In a countably tight space, countably compact subspaces are closed [3]. Closed subspaces of a space satisfying the MOP also satisfy it.…”

Section: More Results In a Model Of Pfa(s)[s]mentioning

confidence: 99%

Some observations on the Baireness of C(X) for a locally compact space X

Tall

2016

Topology and its Applications

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We prove some consistency results concerning the Moving Off Property for locally compact spaces, and thus the question of whether their function spaces are Baire. IntroductionThe Moving Off Property was introduced in [11] to characterize when C k (X) satisfies the Baire Category Theorem, for q-spaces X. Here we shall only be concerned with locally compact spaces (which are q), and so won't define q. We shall assume all spaces are Hausdorff. Definition.A moving off collection for a space X is a collection K of nonempty compact sets such that for each compact L, there is a K ∈ K disjoint from L. A space satisfies the Moving Off Property (MOP) if each moving off collection includes an infinite subcollection with a discrete open expansion.

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“…Proof. In a countably tight space, countably compact subspaces are closed [3]. Closed subspaces of a space satisfying the MOP also satisfy it.…”

Section: More Results In a Model Of Pfa(s)[s]mentioning

confidence: 99%

Some observations on the Baireness of C(X) for a locally compact space X

Tall

2016

Topology and its Applications

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“…Lemma 5.14 [12]. If X is locally compact, locally connected, and countably tight, then X is a topological sum of Type I spaces if and only if every Lindelöf subspace of X has Lindelöf closure.…”

Section: Definitionmentioning

confidence: 99%

Normality Versus Paracompactness in Locally Compact Spaces

Dow¹,

Tall²

2018

Can. j. math.

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This note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing with a coherent Souslin tree. A novel feature of the proof is the use of saturation of the nonstationary ideal on ω 1 , as well as of a strong form of Chang's Conjecture. Together with other improvements, this enables the consistent characterization of locally compact hereditarily paracompact spaces as those locally compact, hereditarily normal spaces that do not include a copy of ω 1 .

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“…Recall a space is ω-bounded if countable sets have compact closures. There are a number of useful variations of ENT; see [7] and [27].…”

Section: 6mentioning

confidence: 99%