Open set recognition (OSR) models need not only discriminate between known classes but also detect unknown class samples unavailable during training. One promising approach is to learn discriminative representations over known classes with strong intra-class similarity and inter-class discrepancy. Then, the powerful class discrimination learned from the known classes can be extended to known and unknown classes. Without appropriate regularization, however, the model may learn representations trivially, collapsing unknown class representations to the known class ones. To resolve this problem, we propose Divergent Angular Representation (DivAR) based on two approaches. Firstly, DivAR maximizes its representational discrimination between known classes via a highly discriminative loss. Secondly, to ensure separation between known and unknown classes in the representation space, DivAR boosts the directional variation of representations over global samples. In addition, self-supervision is leveraged to improve the representation's robustness and extend DivAR to one-class classification. Moreover, unlike other OSR methods that require an extra machinery for inference, DivAR learns and infers in a single module. Extensive experiments on generic image datasets demonstrate the plausibility and effectiveness of DivAR for both OSR and One-Class Classification (OCC) problems.