There exists a polyhedron with infinitely many left neighbors
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- by Danuta Kołodziejczyk PDF
- Proc. Amer. Math. Soc. 129 (2001), 303-309 Request permission
Abstract:
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?References
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Additional Information
- Danuta Kołodziejczyk
- 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
- Email: dkolodz@mimuw.edu.pl
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 303-309
- MSC (2000): Primary 55P55, 55P15
- DOI: https://doi.org/10.1090/S0002-9939-00-05812-3
- MathSciNet review: 1784026