This paper proposes a method to characterize the space explored by a mobile robot during a mission. Because of localization uncertainty, the area osculated by a sensor at a given time is uncertain too. The problem is modeled by using intervals to represent trajectory uncertainties and a "visibility function" to describe the area in view at a given time. A set-inversion method is then applied to compute a "guaranteed visible area" and a "possible visible area" with respect to positioning uncertainty. A bracketing of the actual explored area between a "guaranteed explored area" and a "possible explored area" for the whole mission is finally obtained by respectively taking the union of the guaranteed and possible areas. Results from a simulated underwater exploration mission are presented