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Dimension, Halfspaces, and the Density of Hard Sets

✍ Scribed by Ryan C. Harkins; John M. Hitchcock

Publisher: Springer
Year: 2010
Tongue: English
Weight: 497 KB
Volume: 49
Category: Article
ISSN: 1433-0490
DOI: 10.1007/s00224-010-9288-1

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## Abstract This paper initiates the study of sets in Euclidean spaces ℝ^__n__^ (__n__ ≥ 2) that are defined in terms of the dimensions of their elements. Specifically, given an interval __I__ ⊆ [0, __n__ ], we are interested in the connectivity properties of the set DIM^__I__^ , consisting of all