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General position for closed subsets of euclidean space

✍ Scribed by R.Richard Summerhill

Publisher
Elsevier Science
Year
1973
Weight
890 KB
Volume
3
Category
Article
ISSN
0016-660X

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✦ Synopsis

Let X and Y be "tame" closed subsets of 'Euclidean space Eh having dimensions k and I, respectively. It is shown thst arb.ktrarily close to the identity there exists a homeomorphism h of En onto itself such that dim (Jr(X) f~ Y) G k + I --FL

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G.J. Simmons proved in 1972 that if the regions formed by a Euclidean arrangement of lines in general position are two-colored, with r red regions and g green regions, then r G 2g -2 so that r/g c 2. We use a variant of Simmons' argument to find some analogous estimates in higher dimensional Euclide