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Proposition: Modulus of Continuity is Monotonically Increasing
Let \((X,d_x)\) and \((Y,d_y)\) be metric spaces and let \(f:X\to Y\) be a continuous function on $X$.
The modulus of continuity $\omega_f$ is monotonically increasing, i.e. if $0 \le \delta\le \delta'$ holds for some real numbers $\delta,\delta'$, then $0 \le \omega_f(\delta)\le \omega_f(\delta').$
Table of Contents
Proofs: 1
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983