Open-Set Recognition (OSR) has been emphasizing its capability to reject unknown classes and maintain closed-set performance simultaneously. The primary objective of OSR is to minimize the risk of unknown classes being predicted as one of the known classes. The OSR assumes that unknown classes are present during testing and identifies only one distribution of the unknowns. On the other hand, recognizing unknowns in the domain of interest and outside of the domain of interest will benefit future learning endeavors. These rejected unknown samples in the domain of interest could be leveraged for the further development of deep learning models. We introduce and formalize the open domain-specific space risk to mitigate the recognition of two unknown distributions. To achieve the solution, we propose an initial baseline using quad-channel self-attention reciprocal point learning to mitigate open-space risk and autoencoder to mitigate open domain-specific space risk. We utilize the knowledge in pre-trained models and tune the open-set hyperparameter first before comparing it with other methods as a fair analysis. We also investigate the effect of different pre-trained models in achieving open-set performance. To validate our approach, we tested the model with various domains: garbage, vehicle, household items, and pets. The experimental results demonstrate that our method is robust in rejecting unseen classes while keeping the closed-set accuracy performance at bay. Furthermore, the autoencoder could potentially mitigate open domain-specific space risk in the future, and the determination of pre-trained models highly contributes to the open-set performance.