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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