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COINCIDENCE AND THE COLOURING OF MAPS

Published online by Cambridge University Press:  01 January 1998

JAN M. AARTS  and
ROBBERT J. FOKKINK
JAN M. AARTS
Affiliation:
Technical University Delft, Faculty of Mathematics and Informatics, P.O. Box 5031, 2600 GA Delft, The Netherlands
ROBBERT J. FOKKINK
Affiliation:
Delft Hydraulics, Department of Estuaries and Seas, P.O. Box 177, 2600 MH Delft, The Netherlands
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Abstract

In [8, 6] it was shown that for each k and n such that 2k>n, there exists a contractible k-dimensional complex Y and a continuous map ϕ[ratio ][ ]n→Y without the antipodal coincidence property, that is, ϕ(x)≠ϕ(−x) for all x∈[ ]n. In this paper it is shown that for each k and n such that 2k>n, and for each fixed-point free homeomorphism f of an n-dimensional paracompact Hausdorff space X onto itself, there is a contractible k-dimensional complex Y and a continuous map ϕ[ratio ]X→Y such that ϕ(x)≠ϕ(f(x)) for all x∈X. Various results along these lines are obtained.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 1 , January 1998 , pp. 73 - 79
Copyright
© The London Mathematical Society 1998

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