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328
BOOLEAN RINGS THAT ARE BAIRE SPACES
, 2001
"... Weak completeness properties of Boolean rings are related to the property of being a Baire space (when suitably topologised) and to renorming properties of the Banach spaces of continuous functions on the corresponding Stone spaces. ..."
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Weak completeness properties of Boolean rings are related to the property of being a Baire space (when suitably topologised) and to renorming properties of the Banach spaces of continuous functions on the corresponding Stone spaces.
BAIRE SPACES AND VIETORIS HYPERSPACES
, 2006
"... We prove that if the Vietoris hyperspace CL(X) of all nonempty closed subsets of a space X is Baire, then all finite powers of X must be Baire spaces. In particular, there exists a metrizable Baire space X whose Vietoris hyperspace CL(X) is not Baire. This settles an open problem of R. A. McCoy sta ..."
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We prove that if the Vietoris hyperspace CL(X) of all nonempty closed subsets of a space X is Baire, then all finite powers of X must be Baire spaces. In particular, there exists a metrizable Baire space X whose Vietoris hyperspace CL(X) is not Baire. This settles an open problem of R. A. Mc
On mBaire Spaces
"... In this paper we introduce and study the notions of dense set and set of first category in a space with mstructure. We also introduce the notion of Baire space in a space with mstructure and explore some of its important properties in this setting. Mathematics Subject Classification: 54C08 ..."
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In this paper we introduce and study the notions of dense set and set of first category in a space with mstructure. We also introduce the notion of Baire space in a space with mstructure and explore some of its important properties in this setting. Mathematics Subject Classification: 54C08
PSEUDOCOMPLETENESS AND THE PRODUCT OF BAIRE SPACES
"... The class of pseudocomplete spaces defined by Oxtoby is one of the largest known classes ^ with the property that any member of & is a Baire space and ^ is closed under arbitrary products. Furthermore, all of the classical examples of Baire spaces belong to & * In this paper it is proved t ..."
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Cited by 4 (1 self)
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The class of pseudocomplete spaces defined by Oxtoby is one of the largest known classes ^ with the property that any member of & is a Baire space and ^ is closed under arbitrary products. Furthermore, all of the classical examples of Baire spaces belong to & * In this paper it is proved
The product of a Baire space with a hereditarily Baire metric space is Baire
"... B. Moors1 Abstract. In this paper we prove that the product of a Baire space with a metrizable hereditarily Baire space is again a Baire space. This answers a recent question of J. Chaber and ..."
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B. Moors1 Abstract. In this paper we prove that the product of a Baire space with a metrizable hereditarily Baire space is again a Baire space. This answers a recent question of J. Chaber and
Analytic Baire spaces
"... We generalize to the nonseparable context a theorem of Levi characterizing Baire analytic spaces. This allows us to prove a jointcontinuity result for nonseparable normed groups, previously known only in the separable context. 1 ..."
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Cited by 3 (3 self)
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We generalize to the nonseparable context a theorem of Levi characterizing Baire analytic spaces. This allows us to prove a jointcontinuity result for nonseparable normed groups, previously known only in the separable context. 1
THE GEOMETRY OF BAIRE SPACES
, 2008
"... We introduce the concept of Baire embeddings and we classify them up to C 1+ε conjugacies. We show that two such embeddings are C 1+εequivalent if and only if they have exponentially equivalent geometries. Next, we introduce the class of IFSlike Baire embeddings and we also show that two Hölder eq ..."
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We introduce the concept of Baire embeddings and we classify them up to C 1+ε conjugacies. We show that two such embeddings are C 1+εequivalent if and only if they have exponentially equivalent geometries. Next, we introduce the class of IFSlike Baire embeddings and we also show that two Hölder
SELECTION PRINCIPLES AND BAIRE SPACES
, 2007
"... We prove that if X is a separable metric space with the Hurewicz covering property, then the BanachMazur game played on X is determined. The implication is not true when “Hurewicz covering property” is replaced with “Menger covering property”. ..."
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We prove that if X is a separable metric space with the Hurewicz covering property, then the BanachMazur game played on X is determined. The implication is not true when “Hurewicz covering property” is replaced with “Menger covering property”.
Compact subsets of the Baire space
, 2012
"... Results in this note were obtained in 1994 and reported on at a meeting ..."
RICH FAMILIES, WSPACES AND THE PRODUCT OF BAIRE SPACES
"... Abstract. In this paper we prove a theorem more general than the following. Suppose that X is a Baire space and Y is the product of hereditarily Baire metric spaces then X × Y is a Baire space. ..."
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Abstract. In this paper we prove a theorem more general than the following. Suppose that X is a Baire space and Y is the product of hereditarily Baire metric spaces then X × Y is a Baire space.
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