# A Generalization of the Weierstrass Theorem

### A. Drwalewska

Technical University Lodz, Poland

## Abstract

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 $p$).

## 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