The rapid growth of text-to-image diffusion models has raised concerns about their potential misuse in generating harmful or unauthorized contents. To address these issues, several Concept Erasure methods have been proposed. However, most of them fail to achieve both completeness, i.e., the ability to entirely remove the target concept, and effectiveness, i.e., maintaining image quality. While few recent techniques successfully achieve these goals for NSFW concepts, none could handle narrow concepts such as copyrighted characters or celebrities. Erasing these narrow concepts is critical in addressing copyright and legal concerns. However, erasing them from diffusion models is challenging due to their close distances to non-target neighboring concepts, requiring finer-grained manipulation. In this paper, we introduce Subspace Mapping (SuMa), a novel method specifically designed to achieve both completeness and effectiveness in easing these narrow concepts. SuMa first derives a target subspace representing the concept to be erased and then neutralizes it by mapping it to a reference subspace that minimizes the distance between the two. This mapping ensures the target concept is fully erased while preserving image quality. We conduct extensive experiments with SuMa across four tasks: subclass erasure, celebrity erasure, artistic style erasure, and instance erasure and compare the results with current state-of-the-art methods. Our method not only outperforms those focused on effectiveness in terms of image quality but also achieves comparable results with methods targeting completeness.