


Paper Title:
Purely Unrectifiable Sets with Large Projections
Author(s):
Harold R. Parks
Department of Mathematics,
Oregon State University,
Corvallis, Oregon 973314605,
USA
parks@math.oregonstate.edu
URL: http://www.math.oregonstate.edu/people/view/parks/
Abstract:
For n≥2, we give a construction of a compact subset of that is dispersed enough that it is purely unrectifiable, but that nonetheless has an orthogonal projection that hits every point of an (n1)dimensional unit cube. Moreover, this subset has the additional surprising property that the orthogonal projection onto any straight line in is a set of positive 1dimensional Hausdorff measure.
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