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There exists a polyhedron with infinitely many left neighbors |
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| Authors: | Danuta Kolodziejczyk |
| Affiliation: | Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-950 Warsaw, Poland - Address for correspondence: ul. Jasna 8/18, 00-013 Warsaw, Poland |
| Abstract: | We show that there exists a finite polyhedron |
| Keywords: | Shape homotopy type FANR polyhedron shape domination homotopy domination left neighbor |
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homotopy dominating infinitely many finite polyhedra 
of different homotopy types such that there isn't any homotopy type between 
and 
. This answers negatively the question raised by K. Borsuk in 1975: Does every FANR have only finitely many left neighbors?