The Infimum Hausdorff Dimension of Totally Disconnected Sets of Which Every Projection is an Interval.

2023 · doi:10.21203/rs.3.rs-3490625/v1
preprint OA: closed CC-BY-4.0
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Abstract

Abstract In this paper, we study the orthogonal projections of the Cantor dust sets E⊂R2. The essence of our study centers on the question of how densely a dust-like can be structured while still allowing the sunlight’s shadow to cast an interval. We prove that 1 is the infimum Hausdorff dimension of a totally disconnected set in two-dimensional space with the property that the projection to any line is an interval.

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License: CC-BY-4.0