On the connectivity for Darboux functions
Jan M. Jastrzębski, Mariusz Strześniewski (1985)
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Jan M. Jastrzębski, Mariusz Strześniewski (1985)
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Jack Ceder (1976)
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Sierpinski has shown (Wacław Sierpiński Sur une condition pour qu'un continu soit une courbe jordanienne, Fundamenta Mathematicae I (1920), pp. 44-60) that in order that a closed and connected set of points M should be a continuous curve it is necessary and sufficient that, for every positive number ϵ, the connected point-set M should be the sum of a finite number of closed and connected point-sets each of diameter less than ϵ. It follows that, as applied to point-sets which are closed,...