Abstract
We show that the space of homeomorphisms on the unit interval [0,1], equipped with the topology of uniform convergence, contains a dense subspace of functions that preserve the Hausdorff measure of any subset of certain one-dimensional self-similar sets. We extend the results to a class of Cantor dust type self-similar sets in R2.
Original language | English |
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Article number | 126485 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 516 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1 2022 |
Keywords
- Cantor dust
- Cantor set
- Hausdorff measure
- Homeomorphism
- Self-similar set