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We prove that the low dimensions of a class of Moran sets coincide with their Hausdorff dimensions and obtain a formula for the lower dimensions. Subsequently, we consider some homogeneous… Click to show full abstract
We prove that the low dimensions of a class of Moran sets coincide with their Hausdorff dimensions and obtain a formula for the lower dimensions. Subsequently, we consider some homogeneous Cantor sets which belong to Moran sets and give the counterexamples in which their Assouad dimension is not equal to their upper box dimensions and packing dimensions under the case of not satisfying the condition of the smallest compression ratio .
Keywords:
assouad dimensions;
lower dimensions;
dimensions moran;
dimensions lower;
moran sets
Journal Title: Journal of Mathematics
Year Published: 2020
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Journal Title: Journal of Mathematics
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!