Realizing Stable Pairs of Hahn as Extremal Sections of Separately Continuous Functions
A pair of functions (g,h) on X with g upper semicontinuous, h lower semicontinuous, and g<=h is a pair of Hahn; it is stable when g and h are the pointwise max and min of one sequence of continuous functions. This result characterizes when such a stable pair is exactly the minimal/maximal section pair of a separately continuous function on a product X x Y, proving it holds for compact X, Y with Y scattered and a countable-chain-condition factor, and conversely realizing every stable pair over an infinite completely regular Y.
ON STABLE PAIRS OF HAHN AND EXTREMAL SECTIONS OF SEPARATELY CONTINUOUS FUNCTIONS ON THE PRODUCTS
For a real function f on a product X x Y, the minimal and maximal sections are the pointwise inf and sup over Y, giving functions on X. A pair (g,h) on X is a pair of Hahn if g <= h with g upper semi…