The well-known Weierstrass theorem stating that a real-valued continuous function on a compact set attains its maximum on is generalized. Namely, the space of real numbers is replaced by a set with arbitrary preference relation (in place of the inequality ≤), and the assumption of continuity of is replaced by its monotonic semicontinuity (with respect to the relation ).
Cite this article
A. Drwalewska, A Generalization of the Weierstrass Theorem. Z. Anal. Anwend. 15 (1996), no. 3, pp. 759–763DOI 10.4171/ZAA/727