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weakly monotone

A surjective mapping $f: X \to Y$ between compact spaces is said to be (see [59, Chapter 3 and 4, p. 12-28]) weakly monotone provided that for each subcontinuum Q of Y with the nonempty interior each component the set f-1(Q) is mapped under f onto Q.

Janusz J. Charatonik and Pavel Pyrih
2000-09-21