Proof

(related to Proposition: Preservation of Continuity with Arithmetic Operations on Continuous Functions on a Whole Domain)

This is a simple corollary to the preservation of continuity with arithmetic operations on continuous functions at a point \(a\), because the real functions \(f,g:D\to\mathbb R\) are continuous at every point \(a\in D\), by hypothesis.


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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983