Category and dimensions for cut-out sets |
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Authors: | Ying Xiong Min Wu |
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Institution: | Department of Mathematics, South China University of Technology, Guangzhou 510641, PR China |
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Abstract: | In this paper, we study the modified box dimensions of cut-out sets that belong to a positive, nonincreasing and summable sequence. Noting that the family of such sets is a compact metric space under the Hausdorff metric, we prove that the lower modified box dimension equals zero and the upper modified box dimension equals the upper box dimension for almost all cut-out set in the sense of Baire category. |
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Keywords: | Cut-out set Modified box dimension Baire category |
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