What weak or weakest conditions (on the function and its domain) ensure that a real-valued, not essentially constant function on a real domain has the property that for any y between the functions essential infimum and essential supremum, there exist a pair of disjoint intervals such that the function is larger than y on one and less than y on the other. Piecewise continuity is sufficient. But perhaps there are weaker conditions.
2026-03-26 16:07:07.1774541227
What weak, or weakest, conditions ensure the existence of two intervals such that a function is uniformly larger on one than the other
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