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Coincidence and The Colouring of Maps
Author(s) -
Aarts Jan M.,
Fokkink Robbert J.
Publication year - 1998
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609397003317
Subject(s) - contractible space , mathematics , coincidence , homeomorphism (graph theory) , paracompact space , antipodal point , hausdorff space , continuous map , combinatorics , mathematics subject classification , discrete mathematics , pure mathematics , geometry , medicine , alternative medicine , pathology
In [ 8, 6 ] it was shown that for each k and n such that 2 k > n , there exists a contractible k ‐dimensional complex Y and a continuous map φ: S n → Y without the antipodal coincidence property, that is, φ( x )≠φ(− x ) for all x ∈ S n . In this paper it is shown that for each k and n such that 2 k > 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: X → Y such that φ( x )≠φ( f ( x )) for all x ∈ X . Various results along these lines are obtained. 1991 Mathematics Subject Classication 55M10, 54C05.