Point of view is interesting in Mansfield's "Miss Brill." The opening line indicates clearly for us that the point of view is focalized through a limited third person narrator who tells us about the story by focusing on Miss Brill's experience:
Although it was so brilliantly fine--the blue sky powdered with gold and great spots of light like white wine splashed over the Jardins Publiques-- Miss Brill was glad that she had decided on her fur.
Third person narrators stand outside the story and provide a "bird's eye" view, so to speak, into the events and personalities and the effects of events. These narrators provide objective reports in the narrative that may be more or less objective but certainly quite different from a subjective first person point of view. These narrators may also be more or less distanced in proximity: they may report the narrative through a great emotional distance from events, personalities, and effects or they may report from a near proximity and even comment upon events, personalities and effects.
Limited third person narrators, which are different from omniscient third person narrators, focalize the narrative through the experience of one character (that character may change from time to time in various chapters of a book but is consistent in a short story). This sort of narrator has access to the focalizing character's thoughts, feelings, motives, and inner perceptions and reactions.
In "Miss Brill," the limited third person narrator has a very near proximity and, though objective, provides a report on the stream of consciousness thoughts and reactions of Miss Brill. This stream of consciousness element in the narrator's report is what makes the point of view in "Miss Brill" so interesting: we "hear" what Miss Brill thinks as she thinks it through the narrator's report:
Miss Brill had often noticed--there was something funny about nearly all of them. They were odd, silent, nearly all old, and from the way they stared they looked as though they'd just come from dark little rooms or even--even cupboards!