Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1996-09-30
A Generalization of the Weierstrass TheoremA. Drwalewska (1) Technical University Lodz, Poland
The well-known Weierstrass theorem stating that a real-valued continuous function $f$ on a compact set $K \subset \mathbb R$ attains its maximum on $K$ is generalized. Namely, the space of real numbers is replaced by a set $Y$ with arbitrary preference relation $p$ (in place of the inequality ≤), and the assumption of continuity of $f$ is replaced by its monotonic semicontinuity (with respect to the relation $p$).
Keywords: Multiobjective optimization, maximal points, ($p,p$)-maximal points, monotonically semicontinuous functions, sequentially compact sets
Drwalewska A.: A Generalization of the Weierstrass Theorem. Z. Anal. Anwend. 15 (1996), 759-763. doi: 10.4171/ZAA/727