LARGE INTERSECTION PROPERTIES FOR LIMSUP SETS GENERATED BY RECTANGLES IN COMPACT METRIC SPACES

Nan Ding ()
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Nan Ding: School of Mathematics and Statistics, Huazhong University of Science and Technology, 430074 Wuhan, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 06, 1-13

Abstract: The large intersection classes in real Euclidean spaces have been introduced by Falconer in 1985. First, we generalize Falconer’s large intersection classes to compact metric spaces and show that these classes are closed under countable intersections. Next, we prove that the limsup sets generated by rectangles in a compact metric space enjoy this intersection property under certain full Hausdorff measure assumptions. We also apply our results to high-dimensional Diophantine approximation on fractals.

Keywords: Large Intersection Class; Metric Space; Rectangle (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501371

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