On almost continuous derivations (Q2464608)

A function \(f:\mathbb R\to\mathbb R\) is called additive if \(f(x+y)=f(x)+f(y)\), \(\forall x,y\in\mathbb R\); if in addition, \(f(xy)=xf(y)+yf(x)\), \(\forall x,y\in\mathbb R\), then \(f\) is called a derivation. The main results of the paper are: i) every derivation is the sum of two (Stallings) almost continuous derivations and ii) each derivation is the limit of a sequence (of a transfinite sequence) of almost continuous derivations.