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The drabness of the physical setting in which Jim and Della live creates a contrast with the warmth and richness of their love for each other. The fact that everything outside the flat is "grey" Della watches a "gray cat walking a gray fence in a gray backyard" develops the contrast even further. Inside, we get the sense, Jim and Della's affection creates a welcoming love nest, in spite of the flat's humble nature. Outside, it's a cold, gray world, and one that is about as uncaring as Madame Sofronie.
As for the larger "where and when," we don't have much in the way of specifics. It is possible the story is set in a city – "flats" are the kind of thing you often associate with cities – but not necessarily so (the flat has a backyard, which is a little less urban). From the "gas" which Della lights and the gadgets she has (i.e., a stove and curling irons), it is a safe bet that the story is set just about the time O. Henry wrote it
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