While convolutional neural networks have brought significant advances in robot vision, their ability is often limited to closed world scenarios, where the number of semantic concepts to be recognized is determined by the available training set. Since it is practically impossible to capture all possible semantic concepts present in the real world in a single training set, we need to break the closed world assumption, equipping our robot with the capability to act in an open world. To provide such ability, a robot vision system should be able to (i) identify whether an instance does not belong to the set of known categories (i.e. open set recognition), and (ii) extend its knowledge to learn new classes over time (i.e. incremental learning). In this work, we show how we can boost the performance of deep open world recognition algorithms by means of a new loss formulation enforcing a global to local clustering of class-specific features. In particular, a first loss term, i.e. global clustering, forces the network to map samples closer to the class centroid they belong to while the second one, local clustering, shapes the representation space in such a way that samples of the same class get closer in the representation space while pushing away neighbours belonging to other classes. Moreover, we propose a strategy to learn class-specific rejection thresholds, instead of heuristically estimating a single global threshold, as in previous works. Experiments on RGB-D Object and Core50 datasets show the effectiveness of our approach.