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Reference28 articles.
1. National Research Fellow in Mathematics.
2. Cf. Hans Hahn, ?Mengentheoretische Charakterisierung der stetigen Kurve,? Wiener Sitzungsberichte123 (1914), IIa, pp. 2433?2489.
3. IfX andY are distinct points, then asimple continuous arc (for the sake of brevity we shall say simply anarc) fromX toY is defined by Lennes as a closed connected set containingX andY but containing no proper connected subset that contains bothX andY. See N. J. Lennes, ?Curves in non-metrical plane analysis situs with an application in the calculus of variations,? Amer. Journ. of Math.33 (1911), pp. 287?326. IfXY denotes an arc fromX toY, the pointsX andY are said to be theend points of the arc and every other point of the arcXY is said to beinterior to the arc or aninterior point of the arc. The symbolsXY>, denote the setsXY-Y, XY-X andXY-X-Y respectively. The set is called thearc-segment XY.
4. S. Mazuikiewicz, ?Un th�or�me sur les lignes de Jordan,? Fund. Math.2 (1921), pp. 119?130. See Lemma 13, p. 129.
5. Asimple closed curve is the sum of two arcs which have only their end points in common.
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1. Cyclic Elements in Topology, A History;The American Mathematical Monthly;1966-04
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