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# order preserving mapping

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