Raising dimension under all projections
Fundamenta Mathematicae (1994)
- Volume: 144, Issue: 2, page 119-128
- ISSN: 0016-2736
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topCobb, John. "Raising dimension under all projections." Fundamenta Mathematicae 144.2 (1994): 119-128. <http://eudml.org/doc/212018>.
@article{Cobb1994,
abstract = {As a special case of the general question - “What information can be obtained about the dimension of a subset of $ℝ^n$ by looking at its orthogonal projections into hyperplanes?” - we construct a Cantor set in $ℝ^3$ each of whose projections into 2-planes is 1-dimensional. We also consider projections of Cantor sets in $ℝ^n$ whose images contain open sets, expanding on a result of Borsuk.},
author = {Cobb, John},
journal = {Fundamenta Mathematicae},
keywords = {orthogonal projection; hyperplane; convex body; Cantor set},
language = {eng},
number = {2},
pages = {119-128},
title = {Raising dimension under all projections},
url = {http://eudml.org/doc/212018},
volume = {144},
year = {1994},
}
TY - JOUR
AU - Cobb, John
TI - Raising dimension under all projections
JO - Fundamenta Mathematicae
PY - 1994
VL - 144
IS - 2
SP - 119
EP - 128
AB - As a special case of the general question - “What information can be obtained about the dimension of a subset of $ℝ^n$ by looking at its orthogonal projections into hyperplanes?” - we construct a Cantor set in $ℝ^3$ each of whose projections into 2-planes is 1-dimensional. We also consider projections of Cantor sets in $ℝ^n$ whose images contain open sets, expanding on a result of Borsuk.
LA - eng
KW - orthogonal projection; hyperplane; convex body; Cantor set
UR - http://eudml.org/doc/212018
ER -
References
top- [B] K. Borsuk, An example of a simple arc in space whose projection in every plane has interior points, Fund. Math. 34 (1947), 272-277. Zbl0032.31404
- [E] R. Engelking, Dimension Theory, PWN, Warszawa, and North-Holland, Amsterdam, 1978.
- [M] S. Mardešić, Compact subsets of and dimension of their projections, Proc. Amer. Math. Soc. 41 (2) (1973), 631-633. Zbl0272.54030
- [R] Referee's comment
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