Homi-repair under iteration (II): oscillating discontinuities and pre-discontinuities

It is shown that removable and jumping discontinuities for functions having more than one but finitely many discontinuities have a second order C^0 homi-repair. In this paper we study second order C^0 homi-repair of oscillating discontinuities and pre-discontinuities for those functions and give necessary and sufficient conditions for C^0 repair by second order iteration.