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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.
Baire property in product spaces
"... We show that if a product space Π has countable cellularity, then a dense subspace X of Π is Baire provided that all projections of X to countable subproducts of Π are Baire. It follows that if Xi is a dense Baire subspace of a product of spaces having countable piweight, for each i ∈ I, then the p ..."
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We show that if a product space Π has countable cellularity, then a dense subspace X of Π is Baire provided that all projections of X to countable subproducts of Π are Baire. It follows that if Xi is a dense Baire subspace of a product of spaces having countable piweight, for each i ∈ I
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
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
FUNCTIONALLY COUNTABLE SPACES AND BAIRE FUNCTIONS
"... Abstract. The concept of the distinguished sets is applied to the investigation of the functionally countable spaces. It is proved that every Baire function on a functionally countable space has a countable image. This is a positive answer to a question of R. Levy and W. D. Rice. 0. Introduction. T ..."
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Abstract. The concept of the distinguished sets is applied to the investigation of the functionally countable spaces. It is proved that every Baire function on a functionally countable space has a countable image. This is a positive answer to a question of R. Levy and W. D. Rice. 0. Introduction
COMPACTNESS IN THE FIRST BAIRE CLASS AND BAIRE1 OPERATORS
, 2002
"... For a polish space M and a Banach space E let B1(M,E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1(M,E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in ..."
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For a polish space M and a Banach space E let B1(M,E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1(M,E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy
Borel extensions of Baire measures
"... Abstract. We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasiMařík but not Mařík, answering a question of H. Ohta and K. Tamano, and ..."
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, and under P (c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space is Mařík, that under "c is realvalued measurable", a Baire subset of a Mařík space need
ISOMORPHISM PROBLEMS FOR THE BAIRE FUNCTION SPACES OF TOPOLOGICAL SPACES
"... Dedicated to the memory of Professor D. Doitchinov Abstract. Let a compact Hausdorff space X contain a nonempty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα(X) of all bounded realvalued functions of Baire class α on X is a proper subspace of the Banach space B ..."
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Dedicated to the memory of Professor D. Doitchinov Abstract. Let a compact Hausdorff space X contain a nonempty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα(X) of all bounded realvalued functions of Baire class α on X is a proper subspace of the Banach space
On hereditary Baireness of the Vietoris topology
 Topology Appl
, 2001
"... Abstract. It is shown that a metrizable space X, with completely metrizable separable closed subspaces, has a hereditarily Baire hyperspace K(X) of nonempty compact subsets ofX endowed with the Vietoris topology τv. In particular, making use of a construction of Saint Raymond, we show in ZFC that ..."
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Cited by 1 (0 self)
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that there exists a noncompletely metrizable, metrizable space X with hereditarily Baire hyperspace (K(X), τv); thus settling a problem of A. Bouziad. Hereditary Baireness of (K(X), τv) for a Moore space X is also characterized in terms of an auxiliary product space and the strong Choquet game. Finally, using a
On some new ideals on the Cantor and Baire spaces
 Proc. Am. Math. Soc
, 1998
"... Abstract. We define and investigate some new ideals of subsets of the Cantor space and the Baire space. We show that combinatorial properties of these ideals can be described by the splitting and reaping cardinal numbers. We show that there exist perfect Luzin sets for these ideals on the Baire spac ..."
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Cited by 8 (7 self)
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Abstract. We define and investigate some new ideals of subsets of the Cantor space and the Baire space. We show that combinatorial properties of these ideals can be described by the splitting and reaping cardinal numbers. We show that there exist perfect Luzin sets for these ideals on the Baire
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