I was taught, perhaps erroneously, and certainly many decades ago, that the double (em) dash can be used to deal with putting one sentence inside another.
"If f is continuous on the closed interval [a,b] and differentiable" – "Fire!" shouted Professor Smurdley's pet student, and sure enough the waste basket was ablaze – "and differentiable on the open interval (a,b)", continued Smurdley quite unfazed by the interruption.
Is this sentence punctuated correctly?