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CORRECTING THEOREM 1 FROM "WHEN LINES GO BAD IN HYPERSPACE"

CORRECTING THEOREM 1 FROM "WHEN LINES GO BAD IN HYPERSPACE" DEMONSTRATIO MATHEMATICAVol. XLIINo 22009Steven Schlicker, Christopher Bay, A m b e r LembckeCORRECTING THEOREM 1 FROM" W H E N L I N E S GO B A D IN H Y P E R S P A C E "An Incorrect T h e o r e mThis is in regards to the paper "When Lines go bad in hyperspace" byChristopher Bay, Amber Lembcke, and Steven Schlicker which appears inDemonstratio Mathematica, No. 3, Volume 38 (2005), p. 689-701. It hasrecently been brought to our attention that Theorem 1 from this paper is notcorrect. Please note that the main conclusions of the paper do not depend atall on this theorem. However, as the authors we feel it is our responsibilityto bring this erroneous theorem to your attention.As stated in the paper, Theorem 1 intends to demonstrate that there canbe infinitely many elements at a given location between two sets A and B.THEOREM 1. Let A ± B ewith d(B,A) > d(A, B), r = h(A, B),s £ l with 0 < s < r, and t = r — s. If C is a compact subset of (.A)s fl (B)tcontaining <9((^4)s fl ( B ) t ) , then http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

CORRECTING THEOREM 1 FROM "WHEN LINES GO BAD IN HYPERSPACE"

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References (3)

Publisher
de Gruyter
Copyright
© by Steven Schlicker
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2009-0202
Publisher site
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Abstract

DEMONSTRATIO MATHEMATICAVol. XLIINo 22009Steven Schlicker, Christopher Bay, A m b e r LembckeCORRECTING THEOREM 1 FROM" W H E N L I N E S GO B A D IN H Y P E R S P A C E "An Incorrect T h e o r e mThis is in regards to the paper "When Lines go bad in hyperspace" byChristopher Bay, Amber Lembcke, and Steven Schlicker which appears inDemonstratio Mathematica, No. 3, Volume 38 (2005), p. 689-701. It hasrecently been brought to our attention that Theorem 1 from this paper is notcorrect. Please note that the main conclusions of the paper do not depend atall on this theorem. However, as the authors we feel it is our responsibilityto bring this erroneous theorem to your attention.As stated in the paper, Theorem 1 intends to demonstrate that there canbe infinitely many elements at a given location between two sets A and B.THEOREM 1. Let A ± B ewith d(B,A) > d(A, B), r = h(A, B),s £ l with 0 < s < r, and t = r — s. If C is a compact subset of (.A)s fl (B)tcontaining <9((^4)s fl ( B ) t ) , then

Journal

Demonstratio Mathematica – de Gruyter

Published: Apr 1, 2009

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