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There exists a polyhedron with infinitely many left neighbors

Author: Danuta Kolodziejczyk
Journal: Proc. Amer. Math. Soc. 129 (2001), 303-309
MSC (2000): Primary 55P55, 55P15
Published electronically: August 30, 2000
MathSciNet review: 1784026
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We show that there exists a finite polyhedron $P$ homotopy dominating infinitely many finite polyhedra $K_i$ of different homotopy types such that there isn't any homotopy type between $P$ and $K_i$. This answers negatively the question raised by K. Borsuk in 1975: Does every FANR have only finitely many left neighbors?

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Additional Information

Danuta Kolodziejczyk
Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950 Warsaw, Poland; Address for correspondence: ul. Jasna 8/18, 00-013 Warsaw, Poland
Address at time of publication: Department of Mathematics and Informational Sciences, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warsaw, Poland

Keywords: Shape, homotopy type, FANR, polyhedron, shape domination, homotopy domination, left neighbor
Received by editor(s): February 28, 1999
Published electronically: August 30, 2000
Additional Notes: The author would like to thank the Institute of Mathematics of the Polish Academy of Sciences for its support while this work was done.
Communicated by: Ralph Cohen
Article copyright: © Copyright 2000 American Mathematical Society