Contrastive Language-Image Pre-training (CLIP) has demonstrated great potential in realizing open-vocabulary image classification in a matching style, because of its holistic use of natural language supervision that covers unconstrained real-world visual concepts. However, it is, in turn, also difficult to evaluate and analyze the openness of CLIP-like models, since they are in theory open to any vocabulary but the actual accuracy varies. To address the insufficiency of conventional studies on openness, we resort to an incremental view and define the extensibility, which essentially approximates the model’s ability to deal with new visual concepts, by evaluating openness through vocabulary expansions. Our evaluation based on extensibility shows that CLIP-like models are hardly truly open and their performances degrade as the vocabulary expands to different degrees. Further analysis reveals that the over-estimation of openness is not because CLIP-like models fail to capture the general similarity of image and text features of novel visual concepts, but because of the confusion among competing text features, that is, they are not stable with respect to the vocabulary. In light of this, we propose to improve the openness of CLIP from the perspective of feature space by enforcing the distinguishability of text features. Our method retrieves relevant texts from the pre-training corpus to enhance prompts for inference, which boosts the extensibility and stability of CLIP even without fine-tuning.