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The ability to evolve is fundamental for any valuable autonomous agent whose knowledge cannot remain limited to that injected by the manufacturer. Consider for example a home assistant robot: it should be able to incrementally learn new object categories when requested, but also to recognize the same objects in different environments (rooms) and poses (hand-held/on the floor/above furniture), while rejecting unknown ones. Despite its importance, this scenario has started to raise interest in the robotic community only recently and the related research is still in its infancy, with existing experimental testbeds but no tailored methods. With this work, we propose the first learning approach that deals with all the previously mentioned challenges at once by exploiting a single contrastive objective. We show how it learns a feature space perfectly suitable to incrementally include new classes and is able to capture knowledge which generalizes across a variety of visual domains. Our method is endowed with a tailored effective stopping criterion for each learning episode and exploits a self-paced thresholding strategy that provides the classifier with a reliable rejection option. Both these novel contributions are based on the observation of the data statistics and do not need manual tuning. An extensive experimental analysis confirms the effectiveness of the proposed approach in establishing the new state-of-the-art. The code is available at https://github.com/FrancescoCappio/Contrastive_Open_World.