A Generalization of the Weierstrass Theorem

  • A. Drwalewska

    Technical University Lodz, Poland


The well-known Weierstrass theorem stating that a real-valued continuous function ff on a compact set KRK \subset \mathbb R attains its maximum on KK is generalized. Namely, the space of real numbers is replaced by a set YY with arbitrary preference relation pp (in place of the inequality ≤), and the assumption of continuity of ff is replaced by its monotonic semicontinuity (with respect to the relation pp).

Cite this article

A. Drwalewska, A Generalization of the Weierstrass Theorem. Z. Anal. Anwend. 15 (1996), no. 3, pp. 759–763

DOI 10.4171/ZAA/727