Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Multigeometric sequences and Cantorvals

100%

Bartoszewicz A., Filipczak M., Szymonik E.

Open Mathematics

2014

tom 12

nr 7

1000-1007

For a sequence x ∈ l 1\c 00, one can consider the achievement set E(x) of all subsums of series Σn=1∞ x(n). It is known that E(x) has one of the following structures: a finite union of closed intervals, a set homeomorphic to the Cantor set, a set homeomorphic to the set T of subsums of Σn=1∞ x(n) where c(2n − 1) = 3/4n and c(2n) = 2/4n (Cantorval). Based on ideas of Jones and Velleman [Jones R., Achievement sets of sequences, Amer. Math. Monthly, 2011, 118(6), 508–521] and Guthrie and Nymann [Guthrie J.A., Nymann J.E., The topological structure of the set of subsums of an infinite series, Colloq. Math., 1988, 55(2), 323–327] we describe families of sequences which contain, according to our knowledge, all known examples of x with E(x) being Cantorvals.

A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension

100%

David G., Snipes M.

Analysis and Geometry in Metric Spaces

2013

tom 1

36-41

We give a non-probabilistic proof of a theorem of Naor and Neiman that asserts that if (E, d) is a doubling metric space, there is an integer N > 0, depending only on the metric doubling constant, such that for each exponent α ∈ (1/2; 1), one can find a bilipschitz mapping F = (E; dα ) ⃗ ℝ RN.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Open Mathematics

1 Bartoszewicz A.

1 David G.

1 Filipczak M.

1 Snipes M.

1 Szymonik E.

1 2014

1 2013

Wyniki wyszukiwania

Multigeometric sequences and Cantorvals

A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension