Displaying similar documents to “Sum-sets of small upper density”

On relations between f -density and ( R ) -density

Václav Kijonka (2007)

Acta Mathematica Universitatis Ostraviensis

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In this paper it is discus a relation between f -density and ( R ) -density. A generalization of Šalát’s result concerning this relation in the case of asymptotic density is proved.

Asymptotic density, computable traceability, and 1-randomness

Uri Andrews, Mingzhong Cai, David Diamondstone, Carl Jockusch, Steffen Lempp (2016)

Fundamenta Mathematicae

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Let r ∈ [0,1]. A set A ⊆ ω is said to be coarsely computable at density r if there is a computable function f such that {n | f(n) = A(n)} has lower density at least r. Our main results are that A is coarsely computable at density 1/2 if A is computably traceable or truth-table reducible to a 1-random set. In the other direction, we show that if a degree a is hyperimmune or PA, then there is an a-computable set which is not coarsely computable at any positive density.

Category theorems concerning Z-density continuous functions

K. Ciesielski, L. Larson (1991)

Fundamenta Mathematicae

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The ℑ-density topology T ℑ on ℝ is a refinement of the natural topology. It is a category analogue of the density topology [9, 10]. This paper is concerned with ℑ-density continuous functions, i.e., the real functions that are continuous when the ℑ-densitytopology is used on the domain and the range. It is shown that the family C ℑ of ordinary continuous functions f: [0,1]→ℝ which have at least one point of ℑ-density continuity is a first category subset of C([0,1])= f: [0,1]→ℝ: f is continuous...