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Geometric Realization of a Bellamy Continuum
Author(s) -
Fearnley Lawrence,
Wright David G.
Publication year - 1993
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/blms/25.2.177
Subject(s) - mathematics , indecomposable module , realization (probability) , pure mathematics , property (philosophy) , fixed point , discrete mathematics , mathematical analysis , statistics , philosophy , epistemology
A geometric realization of a tree‐like continuum T consisting of a Cantor set of arcs in the form of a fan together with an indecomposable chainable continuum is constructed, and it is shown that T does not have the fixed point property. This complements work of Bellamy on the notable question of the existence of acyclic continua without the fixed point property.