The Coincidence Set of Generalized Lines and Generalized Monotone Functions

Abstract We investigate the coincidence set of generalized lines and generalized monotone functions, when these notions are induced by an n -parameter Beckenbach family. It turns out that the coincidence set is either an interval or a finite set of at most n elements. Moreover, we show that this set can have exactly k elements if $$k\in \{1,\dots ,n\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>{</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> and the underlying family is an extended and complete Chebyshev-system.