Slowly Oscillating Continuity

A function is continuous if and only if, for each point 0 in the domain, lim→∞()=(0), whenever lim→∞=0. This is equivalent to the statement that (()) is a convergent sequence whenever () is convergent. The concept of slowly oscillating continuity is defined in the sense that a function is slowly oscillating continuous if it transforms slowly oscillating sequences to slowly oscillating sequences, that is, (()) is slowly oscillating whenever () is slowly oscillating. A sequence () of points in is slowly oscillating if lim→1