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Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr

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The Street stretched away north and south in two lines of ancient houses that seemed to meet in the distance. The man found it infinitely inviting. It had the well-worn look of an old coat, shabby but comfortable. The thought of coming there to live pleased him. Surely here would be peace—long evenings in which to read, quiet nights in which to sleep and forget. It was an impression of home, really, that it gave. The man did not know that, or care particularly. He had been wandering about a long time—not in years, for he was less than thirty. But it seemed a very long time.
There was a house across and a little way down the Street, with a card in the window that said: “Meals, twenty-five cents.” Evidently the midday meal was over; men who looked like clerks and small shopkeepers were hurrying away. The Nottingham curtains were pinned back, and just inside the window a throaty barytone was singing: