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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper Title:
Purely Unrectifiable Sets with Large Projections
Author(s):
Harold R. Parks
Department of Mathematics,
Oregon State University,
Corvallis, Oregon 97331--4605,
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 (n-1)-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
1-dimensional Hausdorff measure.
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