Displaying similar documents to “The space of Whitney levels is homeomorphic to l 2 ”

Carathéodory balls and norm balls in H p , n = z ∈ ℂ n : ∥ z ∥ p < 1

Binyamin Schwarz, Uri Srebro (1996)

Banach Center Publications

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It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on H p , n = z ∈ ℂ n : ∥ z ∥ p < 1 which are balls with respect to the complex l p norm in ℂ n are those centered at the origin.

Embedding lattices in the Kleene degrees

Hisato Muraki (1999)

Fundamenta Mathematicae

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Under ZFC+CH, we prove that some lattices whose cardinalities do not exceed ℵ 1 can be embedded in some local structures of Kleene degrees.

On inhomogeneous Diophantine approximation and the Nishioka-Shiokawa-Tamura algorithm

Takao Komatsu (1998)

Acta Arithmetica

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We obtain the values concerning ( θ , ϕ ) = l i m i n f | q | → ∞ | q | ‖ q θ - ϕ ‖ using the algorithm by Nishioka, Shiokawa and Tamura. In application, we give the values (θ,1/2), (θ,1/a), (θ,1/√(ab(ab+4))) and so on when θ = (√(ab(ab+4)) - ab)/(2a) = [0;a,b,a,b,...].

The exceptional set of Goldbach numbers (II)

Hongze Li (2000)

Acta Arithmetica

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1. Introduction. A positive number which is a sum of two odd primes is called a Goldbach number. Let E(x) denote the number of even numbers not exceeding x which cannot be written as a sum of two odd primes. Then the Goldbach conjecture is equivalent to proving that E(x) = 2 for every x ≥ 4. E(x) is usually called the exceptional set of Goldbach numbers. In [8] H. L. Montgomery and R. C. Vaughan proved that E ( x ) = O ( x 1 - Δ ) for some positive constant Δ > 0 . I n [ 3 ] C h e n a n d P a n p r o v e d t h a t o n e c a n t a k e Δ > 0 . 01 . I n [ 6 ] , w e p r o v e d t h a t E ( x ) = O ( x 0 . 921 ) . In this paper we prove the following...