New proofs of the consistency of the normal moore space conjecture I

Dow, Alan; Tall, Franklin D.; Weiss, William

doi:10.1016/0166-8641(90)90013-r

Cited by 38 publications

(17 citation statements)

References 11 publications

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“…In Cohen's original model for the negation of the Continuum Hypothesis (CH), and indeed in any model obtained by adding ℵ 2 Cohen reals to a model of ZFC, every locally compact normal space is ℵ 1 -cwH. This well-known fact can be shown by applying the proof technique of [W,Theorem 3] to [DTW,Theorem 1.4].…”

Section: Definition Let κ Be a Cardinal Number A Space X Is Weakly mentioning

confidence: 79%

Cardinal restrictions on some homogeneous compacta

Juhász

Nyikos

Szentmiklóssy

2005

Proc. Amer. Math. Soc.

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Abstract. We give restrictions on the cardinality of compact Hausdorff homogeneous spaces that do not use other cardinal invariants, but rather covering and separation properties. In particular, we show that it is consistent that every hereditarily normal homogeneous compactum is of cardinality c. We introduce property wD(κ), intermediate between the properties of being weakly κ-collectionwise Hausdorff and strongly κ-collectionwise Hausdorff, and show that if X is a compact Hausdorff homogeneous space in which every subspace has property wD(ℵ 1 ), then X is countably tight and hence of cardinality ≤ 2 c . As a corollary, it is consistent that such a space X is first countable and hence of cardinality c. A number of related results are shown and open problems presented.

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Section: Definition Let κ Be a Cardinal Number A Space X Is Weakly mentioning

confidence: 79%

Cardinal restrictions on some homogeneous compacta

Juhász

Nyikos

Szentmiklóssy

2005

Proc. Amer. Math. Soc.

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“…They are named in honor of Alan Dow who discovered their existence in connection with his work on remote points in Stone-Čech remainders. A proof of their existence can be found in [DTW90a]. Since the proof itself has not had any applications in our work, we omit it.…”

Section: Preservation Under Forcingmentioning

confidence: 99%

“…This technique was introduced in [DTW90a] as part of a reflection + forcing proof of the consistency of the Normal Moore Space Conjecture, and has found several applications since: [GJT98], [Iwa07], [ST], [Kad]. It almost -but not quite -yields a ground model refinement for an open cover in a forcing extension.…”

Section: Preservation Under Forcingmentioning

confidence: 99%

Some problems and techniques in set-theoretic topology

Tall¹

2011

Set Theory and Its Applications

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“…Problem 17 asks whether it is really necessary to use something different from co\ at all. Fleissner showed in 1977 [8] that it is consistent that normal first countable spaces are collectionwise normal with respect to copies of o)\ by collapsing an inaccessible in a model of the constructible universe (see also [6]). I think that the techniques that one would have to develop in order to solve these questions would be useful in many areas of general topology, and thus worth the effort.…”

Section: (Ve£[b\^mentioning

confidence: 99%

Separation and Coding

Watson¹

1994

Transactions of the American Mathematical Society

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Abstract. We construct a normal collectionwise Hausdorff space which is not collectionwise normal with respect to copies of [0,1]. We do this by developing a general theory of coding properties into topological spaces. We construct a para-Lindelöf regular space in which para-Lindelöf is coded directly rather than (T-para-Lindelöf and normal. We construct a normal collectionwise Hausdorff space which is not collectionwise normal in which collectionwise Hausdorff is coded directly rather than obtained as a side-effect to countable approximation. We also show that the Martin's axiom example of a normal space which is not collectionwise Hausdorff is really just a kind of "dual" of Bing's space.

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New proofs of the consistency of the normal moore space conjecture I

Cited by 38 publications

References 11 publications

Cardinal restrictions on some homogeneous compacta

Cardinal restrictions on some homogeneous compacta

Some problems and techniques in set-theoretic topology

Separation and Coding

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