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 \(a\in D\).
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
Example, \(D\) could be a real interval \(I\in \mathbb R\), or all real numbers \(\mathbb R\), or any other subset of real numbers. ↩