REMARKS ON DIMENSIONS OF CARTESIAN PRODUCT SETS
Keyword(s):
Given metric spaces [Formula: see text] and [Formula: see text], it is well known that [Formula: see text] [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] denote the Hausdorff, packing, lower box-counting, and upper box-counting dimension of [Formula: see text], respectively. In this paper, we shall provide examples of compact sets showing that the dimension of the product [Formula: see text] may attain any of the values permitted by the above inequalities. The proof will be based on a study on dimension of products of sets defined by digit restrictions.
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1950 ◽
Vol 69
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pp. 232-232
1975 ◽
Vol 78
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pp. 483-491
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1954 ◽
Vol 5
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1996 ◽
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pp. 535-546
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1953 ◽
Vol 49
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pp. 437-440
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2015 ◽
Vol 40
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pp. 449
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1952 ◽
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pp. 295-304
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