Before revision:  In this paper, we study an online version of UC in L_2, which we call as Online Unit Covering (OUC)in L_2, or, simply Online Unit Covering (OUC). In OUC, the points arrive online sequentially. Once a point p arrives, a decision needs to be taken - either assign p to a previously placed disk (if possible)or place a new disk to cover p since none of the previously placed disks can cover p. In this setup, once a disk is placed, its placement cannot be altered in future. Also, the points remain at their places forever.
After revision:  In this paper, we work in \mathbb{R