Results 281 to 290 of about 606,802 (315)

Random Closed Sets

2007
Concepts and results involving random sets appeared in probabilistic and statistical literature long time ago. The origin of the modern concept of a random set goes as far back as the seminal book by A.N. Kolmogorov [22] (first published in 1933) where he laid out the foundations of probability theory. He wrote [22, p.
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Covering analytic sets by families of closed set

Journal of Symbolic Logic, 1994
AbstractWe prove that for every familyIof closed subsets of a Polish space eachset can be covered by countably many members ofIor else contains a nonemptyset which cannot be covered by countably many members ofI. We prove an analogous result forκ-Souslin sets and show that ifA#exists for anyA⊂ωω, then the above result is true forsets.
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Effectively closed sets and enumerations

Archive for Mathematical Logic, 2008
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Paul Brodhead 0001, Douglas A. Cenzer
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On the intersection of closed unbounded sets

Journal of Symbolic Logic, 1986
AbstractForcing extensions yield models of ZFC in which a long sequence of club subsets of ω1, has the following property: every subsequence of size ℵ1, has a finite intersection.
Uri Abraham, Saharon Shelah
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On the Sum of Roots of a Closed Set

Journal of Mathematical Sciences, 2004
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On Ω-closed sets and Ωs-closed sets in topological spaces

Acta Mathematica Hungarica, 2005
New classes of sets called Ω-closed sets and Ωs-closed sets are introduced and studied. Also, we introduce and study Ω-continuous functions and Ωs-continuous functions and prove pasting lemma for these functions. Moreover, we introduce classes of topological spaces Ω-T1/2 and Ω-Ts.
Takashi Noiri, Osama Rashed Sayed
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Adding a closed unbounded set

The Journal of Symbolic Logic, 1976
The extreme interest of set theorists in the notion of “closed unbounded set” is epitomized in the following well-known theorem:Theorem A. For any regular cardinal κ > ω, the intersection of any two closed unbounded subsets of κ is closed and unbounded.The proof of this theorem is easy and in fact yields a stronger result, namely that for any ...
James E. Baumgartner, Leo Harrington, E. M. Kleinberg   +2 more
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The Character of Certain Closed Sets

Canadian Journal of Mathematics, 1984
Let X be a topological space and let A ⊂ X. The character of A in X is the minimal cardinal of a base for the neighborhoods of A in X. Previous studies have shown that the character of certain subsets of X (or of X2) is related to compactness conditions on X. For example, in [12], Ginsburg proved that if the diagonalof a space X has countable character
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Forcing closed unbounded sets

Journal of Symbolic Logic, 1983
AbstractWe discuss the problem of finding forcing posets which introduce closed unbounded subsets to a given stationary set.
Uri Abraham, Saharon Shelah
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Closed and convex fuzzy sets

Fuzzy Sets and Systems, 2000
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