Hi I was trying to describe a function (see picture).
I want to say that it is discontinuous from an analytic point of view. Because $ \lim_{x \to -1^- }f(x) \ne \lim_{x \to -1^+ }f(x) $
Now from a fixed point theory point of view this function is continuous. Because sup(f(x)) = f(sup(x)) is true for every x in any subset X of the functions domain. Which makes it continuous.
The terminology is confusing because the function is discontinuous from an analytic point of view but continuous in the context of fixed point theory. Is there any way/terminology to distinguish between the two?