Fixed Point Property for Monotone Mappings of Hereditarily Stratified
نویسنده
چکیده
A continuum means comp6lct, connected metric space. A hereditarily unicoherent and arcwise connected continuum is called a dendroid. It follows that it is hereditarily decomposable ([2], (47), p. 239). A hereditarily unicoherent and hereditarily decomposable continuum is said to be a A.-dendroid. Thus, every dendroid is a }.-dendroid and an arcwise connected A.-dendroid is a dendroid. Note that every subcontinuum of a /.-dendroid is a A.-dendroid. It is known that for every A.-dendroid X there exists an upper semi-continuous decomposition (called the canonical decomposition, [5], p. 013) of X into continua Sa (called strata of X) such that the hyperspace of this decomposition is a dendroid Ll-;and such that it is the finest possible decomposition among all upper semicontinuous decompositions of X into continua, hyperspaces of which are dendroids ([5], theorems I, 5 and 6). If X is a dendroid, then the canonical deComposition is a trivial one into points, and if X is an irreducible continuum, then strata of X are tranches in the sense of Kuratowski ([11], §43, IV, p. 139). The monotone mapping f{J of X onto Ll defined by
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