- A complete analysis must build on the implicit function theorem .
- By the corollary to theorem 4. 3, the origin is asymptotically stable .
- All this leads up to the most fundamental of theorems of calculus .
- The assertion is known as the closed graph theorem for hilbert spaces .
- The remarkable part of karatowski's theorem is the "only if" part .
- The power of the greeks to divine theorems and proofs is attested .
- The proof of this theorem was communicated by pietro abbati to ruffini .
- The theorems should be deduced from axioms by purely logical arguments .
- The culmination of the work on singularities is two famous transformation theorems .
- All forms of reciprocal theorems apply to structures which behave linearly .