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

DOI:
https://doi.org/10.1090/S0002-9939-00-05812-3

Published electronically:
August 30, 2000

MathSciNet review:
1784026

Full-text PDF

Abstract | References | Similar Articles | Additional Information

We show that there exists a finite polyhedron 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?

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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

Email:
dkolodz@mimuw.edu.pl

DOI:
https://doi.org/10.1090/S0002-9939-00-05812-3

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