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For each point of a continuum equipped with an
arc-structure
we define a partial
order by letting whenever
. Let and be continua with fixed
arc-structures and , respectively. We say that a
surjective mapping
is a -*mapping*
provided that in implies that
in . If, in addition,
,
, and is a retraction, then is
called a -*retraction* (or -*preserving
retraction*). The concept of a -*mapping* is
defined in a similar manner (with
implied by
). For *order preserving mapping*s see e.g.
[Fugate et al. 1981, I.7, p. 553].

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*Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih*

*2001-11-30*