A few remarks about equality of indicatrices of two functions and a conjecture. (English) Zbl 0942.26008

Summary: Having defined for a couple of functions non co-supportivity in a given direction, we construct for any finite set of directions a couple \(f\) and \(g\) of possibly very regular, continuous, except at finite many points, functions, which in any of these directions are non co-supportive and have the same indicatrix. Adding the requirement that both be continuous (on the joint interval of definition), we are still able to produce such a construction for two directions, but two seems to be the limit: it seems that such a result could not be obtained for three directions.


26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable