Abstract:Our main result asserts that, under some assumptions, the uniformly-to-order continuity of an order bounded orthogonally additive operator between vector lattices together with its horizontally-to-order continuity implies its order continuity (we say that a mapping f : E → F between vector lattices E and F is horizontally-to-order continuous provided f sends laterally increasing order convergent nets in E to order convergent nets in F, and f is uniformly-to-order continuous provided f sends uniformly convergen… Show more
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