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Connectedness properties of dimension level sets

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Title: Connectedness properties of dimension level sets
Authors: Turetsky, Daniel1 dturets@gmail.com
Source: Theoretical Computer Science. Jul2011, Vol. 412 Issue 29, p3598-3603. 6p.
Subjects: Point set theory, Dimensions, Mathematical proofs, Set theory, Mathematical analysis, Computational mathematics
Abstract: Abstract: We prove that the set of all points of effective Hausdorff dimension 1 in is connected, and simultaneously that the complement of this set is not path-connected when . [Copyright &y& Elsevier]
Copyright of Theoretical Computer Science is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 60790449
AccessLevel: 6
PubType: Academic Journal
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  Data: Abstract: We prove that the set of all points of effective Hausdorff dimension 1 in is connected, and simultaneously that the complement of this set is not path-connected when . [Copyright &y& Elsevier]
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  Data: <i>Copyright of Theoretical Computer Science is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.tcs.2011.03.006
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      – Code: eng
        Text: English
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      – SubjectFull: Point set theory
        Type: general
      – SubjectFull: Dimensions
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      – SubjectFull: Mathematical proofs
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      – SubjectFull: Set theory
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      – SubjectFull: Computational mathematics
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      – TitleFull: Connectedness properties of dimension level sets
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              Text: Jul2011
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