Results 271 to 280 of about 132,858 (314)
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Canadian Journal of Mathematics, 1983
In 1979 Edgar asked for a characterization of those completely regular Hausdorff topological spaces X which have the property that any Boolean σ-homomorphism from the Baire σ-field of X into the measure algebra of an arbitrary complete probability space can be realized by a measurable point-mapping. Those spaces X will be called homomorphism-compact or,
Babiker, A. G. A. G., Graf, S.
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In 1979 Edgar asked for a characterization of those completely regular Hausdorff topological spaces X which have the property that any Boolean σ-homomorphism from the Baire σ-field of X into the measure algebra of an arbitrary complete probability space can be realized by a measurable point-mapping. Those spaces X will be called homomorphism-compact or,
Babiker, A. G. A. G., Graf, S.
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Locally compact, ω1-compact spaces
Annals of Pure and Applied LogicAn $ω_1$-compact space is a space in which every closed discrete subspace is countable. We give various general conditions under which a locally compact, $ω_1$-compact space is $σ$-countably compact, i.e., the union of countably many countably compact spaces. These conditions involve very elementary properties.
Nyikos, Peter, Zdomskyy, Lyubomyr
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Mathematika, 1999
Summary: A (countably) compact measure is one which is inner regular with respect to a (countably) compact class of sets. This note characterizes compact probability measures in terms of the representation of Boolean homomorphisms of their measure algebras, and shows that the same ideas can be used to give a direct proof of J.
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Summary: A (countably) compact measure is one which is inner regular with respect to a (countably) compact class of sets. This note characterizes compact probability measures in terms of the representation of Boolean homomorphisms of their measure algebras, and shows that the same ideas can be used to give a direct proof of J.
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Canadian Mathematical Bulletin, 1973
In 1962, J. M. G. Fell [5] indicated the important role played by certain topological spaces which, though locally compact in a specialized sense, do not, in general, satisfy even the weakest separation axiom. He called them "locally compact". These were called "punktal kompakt" by Flachsmeyer [6] and to avoid confusion, we shall call them pointwise ...
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In 1962, J. M. G. Fell [5] indicated the important role played by certain topological spaces which, though locally compact in a specialized sense, do not, in general, satisfy even the weakest separation axiom. He called them "locally compact". These were called "punktal kompakt" by Flachsmeyer [6] and to avoid confusion, we shall call them pointwise ...
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Rendiconti del Circolo Matematico di Palermo, 2005
A minimal structure \(m\) on a set \(X\) is a subset of the power set of \(X\) such that \(\varnothing,X\in m\). Compactness and continuity of topological spaces, as well as a number of other notions such as Hausdorff and regular, extend in the obvious way to minimal structures by replacing the topology by any minimal structure.
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A minimal structure \(m\) on a set \(X\) is a subset of the power set of \(X\) such that \(\varnothing,X\in m\). Compactness and continuity of topological spaces, as well as a number of other notions such as Hausdorff and regular, extend in the obvious way to minimal structures by replacing the topology by any minimal structure.
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Acta Mathematica Hungarica, 2001
For an infinite cardinal \(\kappa\), \(\kappa^+\) denotes the smallest cardinal greater than \(\kappa\). A space \(X\) is called finally \(\kappa^+\)-compact if every open cover of \(X\) has a subcover with cardinality \(\leq\kappa\). The authors define weakly \(\kappa\overline{\theta}\)-refinable spaces and study conditions under which a countably ...
Ergun, N., Noiri, T.
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For an infinite cardinal \(\kappa\), \(\kappa^+\) denotes the smallest cardinal greater than \(\kappa\). A space \(X\) is called finally \(\kappa^+\)-compact if every open cover of \(X\) has a subcover with cardinality \(\leq\kappa\). The authors define weakly \(\kappa\overline{\theta}\)-refinable spaces and study conditions under which a countably ...
Ergun, N., Noiri, T.
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2009
Abstract The subject matter of this chapter is probably the most important single topic in this book. There is more than one way of framing the definition of compactness. The definition in this chapter is appropriate for topological spaces. Another important definition, which works well in metric spaces, will be studied in Chapter 14 and
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Abstract The subject matter of this chapter is probably the most important single topic in this book. There is more than one way of framing the definition of compactness. The definition in this chapter is appropriate for topological spaces. Another important definition, which works well in metric spaces, will be studied in Chapter 14 and
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Extra Countably Compact Spaces
Canadian Mathematical Bulletin, 1983AbstractA completely regular HausdorfT space is extra countably compact if every infinite subset of βX has an accumulation point in X. It is a theorem of Comfort and Waiveris that if X either an F-space or realcompact (topologically complete), then there is a set {Pξ:ξ<2C} of extra countably compact (countably compact) subspaces of αX such that Pξ ∩
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