Existing open set recognition (OSR) methods are typically designed for static scenarios, where models aim to classify known classes and identify unknown ones within fixed scopes. This deviates from the expectation that the model should incrementally identify newly emerging unknown classes from continuous data streams and acquire corresponding knowledge. In such evolving scenarios, the discriminability of OSR decision boundaries is hard to maintain due to restricted access to former training data, causing severe inter-class confusion. To solve this problem, we propose retentive angular representation learning (RARL) for incremental open set recognition (IOSR). In RARL, unknown representations are encouraged to align around inactive prototypes within an angular space constructed under the equiangular tight frame, thereby mitigating excessive representation drift during knowledge updates. Specifically, we adopt a virtual-intrinsic interactive (VII) training strategy, which compacts known representations by enforcing clear inter-class margins through boundary-proximal virtual classes. Furthermore, a stratified rectification strategy is designed to refine decision boundaries, mitigating representation bias and feature space distortion caused by imbalances between old/new and positive/negative class samples. We conduct thorough evaluations on CIFAR100 and TinyImageNet datasets and establish a new benchmark for IOSR. Experimental results across various task setups demonstrate that the proposed method achieves state-of-the-art performance.