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For each point p of a continuum X equipped with an
arc-structure
we define a partial
order
by letting
whenever
. Let
X
and Y be continua with fixed arc-structures A and B, respectively. We
say that a surjective mapping
is a
-mapping
provided that
in X implies that
in Y.
If, in addition,
,
B = A|(Y x Y), and f is a
retraction,
then f is called a
-retraction (or
- preserving retraction). The concept of a
<p-mapping is defined in a similar manner (with
implied by
). For order preserving mappings see e.g.
[42, I.7, p. 553].
Janusz J. Charatonik and Pavel Pyrih
2000-09-21