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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 mappings see e.g.
[Fugate et al. 1981, I.7, p. 553].
Next: ordinary point
Up: Definitions
Previous: order
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30