'What is the name of this function?
I’m looking for the name (or anything written about) a very particular class of mathematical functions. Take a function f(x): R → R and define a new function g(x): R → P(R)/∅ where for all x, f(x) ∈ g(x), but when f(x) has a discontinuous jump, all values between the start and the end of the discontinuity are also included in g(x). When f(x) is continuous, g(x) = {f(x)} is a singleton.
Could anyone point me in the direction of what functions like this are called, or formally defined? It would be a massive help. Thanks in advance :)
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