On discrete properties of continuous monotone functions

Halušková, Emília (2024) On discrete properties of continuous monotone functions. Miskolc Mathematical Notes, 25 (2). pp. 699-712. ISSN 1787-2413

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Abstract

We deal with strictly monotone continuous functions h: I → I, where I is an interval of real numbers. The monounary algebra (I,h) contains at most 4 non-isomorphic components. We derive that there are 10 possibilities only how these components can be combined in (I,h). Two more options are cancelled in case that I = ⟨a,b⟩ for some real numbers a,b,a < b.

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