One of the best things to focus on in this excellent short story is the way that Mansfield skillfully exposes the perception of Miss Brill as she regards her life and then the reality of her lonely, insignificant life that she almost manages to ignore, until the end of the story. Note that this is achieved through the point of view, which is stream-of-consciousness and follows the thoughts of Miss Brill as she sets off for her afternoon trip to the park and then returns home. Clearly, she is a character who deludes herself about her own significance and importance. Perhaps this is most clearly seen when she imagines that the park, and all the people there, including herself, are part of some dramatic play:
They were all on the stage. They weren't only the audience, not only looking on; they were acting. Even she had a part and came every Sunday. No doubt somebody would have noticed if she hadn't been there; she was part of the performance after all.
In Miss Brill's imagination, she is important and has a role, and her absence would be noted. The reality becomes crushingly clear at the end of the story when she returns to "her room like a cupboard" and lets out an involuntary sob. A good thesis statement would therefore be something like:
In "Miss Brill," Mansfield opposes appearances vs. reality to show the intense loneliness of the protagonist.
This thesis statement gives opportunity for the exploration of this theme and how Mansfield resolves the story.