Place representation is a key element in topological maps. This paper presents bubble space - a novel representation for "places" (nodes) in topological maps. The novelties of this model are two-fold: First, a mathematical formalism that defines bubble space is presented. This formalism extends previously proposed bubble memory to accommodate two new variables - varying robot pose and multiple features. Each bubble surface preserves the local S-2 - metric relations of the incoming sensory data from the robot's viewpoint. Secondly, for learning and recognition, bubble surfaces can be transformed into bubble descriptors that are compact and rotationally invariant, while being computable in an incremental manner. The proposed model is evaluated with support vector machine based decision making in two different settings: first with a mobile robot placed in a variety of locations and secondly using benchmark visual data.