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Nonequality of dimensions for metric spaces

1968
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Transactions of the American Mathematical Society
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Introduction. There are three classical set-theoretic notions of dimension; they are [2, p. 153]: Small inductive dimension ( = Menger-Urysohn dimension), denoted by ind such that ind (S) = -1 if S is empty, ind (S) = n if for every point p e S and open set U containing p there is an open set V satisfying p e V <=■ U, ind (boundary of V) S n-l, and ind (S)=n if ind (S)fZn but ind (S) = n-1 is not true. Large inductive dimension (due to Urysohn), denoted by Ind such that Ind (S) = -1 if S is

doi:10.1090/s0002-9947-1968-0227960-2
fatcat:vxww2tha3felllqtbzdca4r7mq