Rough Continuity of Linear Operators

Let and be two linear normed spaces and r ≥ 0. A mapping f:X → Y is called roughly continuous at x ε X w.r.t. the roughness degree r (or shortly: r-continuous at x) if for all ϵ > 0 there exists a δ > 0 such that where and . Under the assumption and r > 0 we show that every linear operator f:X → Y is r-continuous at every point x ε X.