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An uncountable, closed, and non-dense point set each of whose complementary intervals abuts on another one at each of its ends

1923
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Bulletin of the American Mathematical Society
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On page 92 of the 1907 edition of Hobson's The Theory of Functions of a Real Variable, and again on page 113 of the second edition of the same treatise, there occurs the following statement: f "A non-dense closed set is enumerable if its complementary intervals are such that every one of them abuts on another one at each of its ends" To prove this statement, Hobson lets G denote the nondense closed set in question and argues, in part, as follows: "In this case, all the points of G are either

doi:10.1090/s0002-9904-1923-03657-4
fatcat:dky2ykimxvgwppbpq26smgcffu