Geodesic
On a Paper by M. Iosifescu and S. Marcus
Canadian mathematical bulletin, Tome 6 (1963) no. 3, pp. 367-371

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In this paper we will construct an example showing that the problem posed in [1] has a negative answer. Two more theorems on the subject treated in [1] will be included.Let Io = [0, 1], R the reals, and let, for A ⊂ R, Ao be the interior of A. Let {xn} be a sequence in [0, 1> such that 0 = x1 < x2 < ... and lim xn = 1. For each n, let In be closed interval having x as its midpoint (except for n = 1 in which case x1 is the left endpoint of I1) such that In ∩ Im= φ, and the metric density relative to Io of at 1 is zero. Let Jn be a closed interval in In concentric with In (except for n = 1, where J1 has x1 as its left endpoint) whose length is half that of In 
On a Paper by M. Iosifescu and S. Marcus. Canadian mathematical bulletin, Tome 6 (1963) no. 3, pp. 367-371. doi: 10.4153/CMB-1963-031-x
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