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Definition: Continuous Real Functions

Let \(D\subseteq\mathbb R\)¹ and let \(f:D\to\mathbb R\) be a function \(f\) is called continuous on the subset \(D\) (or just continuous, if the domain \(D\) is clear from the context), if \(f\) is continuous at every point \(a\in D\).

Table of Contents

1. Proposition: Preservation of Continuity with Arithmetic Operations on Continuous Functions
2. Proposition: Preservation of Continuity with Arithmetic Operations on Continuous Functions on a Whole Domain
3. Proposition: Fixed-Point Property of Continuous Functions on Closed Intervals
4. Proposition: Comparison of Functional Equations For Linear, Logarithmic and Exponential Growth

Mentioned in:

Corollaries: 1 2 3
Definitions: 4 5
Lemmas: 6
Proofs: 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Propositions: 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
Theorems: 49 50 51 52 53 54 55 56

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References

Bibliography

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

Footnotes