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Zeitschrift für Analysis und ihre Anwendungen

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Volume 15, Issue 3, 1996, pp. 759–763
DOI: 10.4171/ZAA/727

Published online: 1996-09-30

A Generalization of the Weierstrass Theorem

A. Drwalewska[1]

(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