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Between closed sets andg-closed sets
Rendiconti Del Circolo Matematico Di Palermo, 2006In generalized topological spaces \((X,\tau)\) (axioms for open sets are weakened), the authors define \(g\)-closed sets as usually: \(\overline{A}\subset \bigcap \{U;U\in\tau, A\subset U\}\). Using convenient systems for \(\tau\) depending on a given topology \(t\) on \(X\), various known generalized closed sets on \((X,t)\) are obtained.
Takashi Noiri +2 more
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Computability, 2011
A set is called r-closed left-r.e. iff every set r-reducible to it is also a left-r.e. set. It is shown that some but not all left-r.e. cohesive sets are many–one closed left-r.e. sets. Ascending reductions are many–one reductions via an ascending function; left-r.e. cohesive sets are also ascending closed left-r.e. sets.
Sanjay Jain 0001 +2 more
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A set is called r-closed left-r.e. iff every set r-reducible to it is also a left-r.e. set. It is shown that some but not all left-r.e. cohesive sets are many–one closed left-r.e. sets. Ascending reductions are many–one reductions via an ascending function; left-r.e. cohesive sets are also ascending closed left-r.e. sets.
Sanjay Jain 0001 +2 more
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2006
We investigate notions of randomness in the space ${\mathcal {C}}[2^{\mathbb {N}}]$ of nonempty closed subsets of {0,1}ℕ. A probability measure is given and a version of the Martin-Lof Test for randomness is defined. Π02 random closed sets exist but there are no random Π01 closed sets. It is shown that a random closed set is perfect, has measure 0, and
Paul Brodhead 0001 +2 more
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We investigate notions of randomness in the space ${\mathcal {C}}[2^{\mathbb {N}}]$ of nonempty closed subsets of {0,1}ℕ. A probability measure is given and a version of the Martin-Lof Test for randomness is defined. Π02 random closed sets exist but there are no random Π01 closed sets. It is shown that a random closed set is perfect, has measure 0, and
Paul Brodhead 0001 +2 more
openaire +1 more source
2009
The notion of immune sets is extended to closed sets and $\Pi^0_1$ classes in particular. We construct a $\Pi^0_1$ class with no computable member which is not immune. We show that for any computably inseparable sets A and B , the class S (A ,B ) of separating sets for A and B is immune. We show that every perfect thin $\Pi^0_1$ class is immune.
Douglas Cenzer, Rebecca Weber, Guohua Wu
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The notion of immune sets is extended to closed sets and $\Pi^0_1$ classes in particular. We construct a $\Pi^0_1$ class with no computable member which is not immune. We show that for any computably inseparable sets A and B , the class S (A ,B ) of separating sets for A and B is immune. We show that every perfect thin $\Pi^0_1$ class is immune.
Douglas Cenzer, Rebecca Weber, Guohua Wu
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On the ultrafilter of closed, unbounded sets
Journal of Symbolic Logic, 1979Solovay proved in 1967 that the axiom of determinateness implies that the filter C generated by closed and unbounded subsets of ω1 is an ultrafilter. It has long been conjectured that a significant part of the theory of the axiom of determinateness should be provable from the hypothesis that C is an ultrafilter, but even the first step of finding inner
D. A. Martin, William John Mitchell
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Combinatorica, 1984
A subset T of the node set V of a digraph \(G=(V,E)\) is called path-closed if for each v,v'\(\in T\) all nodes lying on directed paths from v to v' also belong to T. The author characterizes the convex hull of the incidence vectors of all path-closed sets by a set of linear inequalities thus turning the problem of finding a maximum path-closed set (in
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A subset T of the node set V of a digraph \(G=(V,E)\) is called path-closed if for each v,v'\(\in T\) all nodes lying on directed paths from v to v' also belong to T. The author characterizes the convex hull of the incidence vectors of all path-closed sets by a set of linear inequalities thus turning the problem of finding a maximum path-closed set (in
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Combinatorica, 2005
A smallest separator in a finite, simple, undirected graph G is a set S ⊆ V (G) such that G–S is disconnected and |S|=κ(G), where κ(G) denotes the connectivity of G.A set S of smallest separators in G is defined to be closed if for every pair S,T ∈ S, every component C of G–S, and every component S of G–T intersecting C either X(C,D) := (V (C) ∩ T ...
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A smallest separator in a finite, simple, undirected graph G is a set S ⊆ V (G) such that G–S is disconnected and |S|=κ(G), where κ(G) denotes the connectivity of G.A set S of smallest separators in G is defined to be closed if for every pair S,T ∈ S, every component C of G–S, and every component S of G–T intersecting C either X(C,D) := (V (C) ∩ T ...
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The Journal of Clinical Ethics, 2011
Published accounts of specific priority-setting projects in healthcare are relatively few. This article chronicles the collaborative efforts of a professional practice lead and a bioethicist to strengthen the priority-setting process for a specific home care service.
Barbara, Russell, Deb, deVlaming
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Published accounts of specific priority-setting projects in healthcare are relatively few. This article chronicles the collaborative efforts of a professional practice lead and a bioethicist to strengthen the priority-setting process for a specific home care service.
Barbara, Russell, Deb, deVlaming
openaire +2 more sources