1. R. L. Moore, A theorem concerning continuous curves, Bull. Amer. Math. Soc., 2d. series,23 (Febr. 1917), S. 233?236. See also H. Tietze, Über stetige Kurven, Jordansche Kurvenbögen und geschlossene Jordansche Kurven, Math. Zeitschr.5 (1919), S. 284?291; and S. Mazurkiewicz, Sur les lignes de Jordan, Fundamenta Mathematicae1 (1920), S. 166?209. In this article, Mazurkiewicz establishes numerous results and indicates that some of them were published earlier in a journal (C. R. Soc. Sc. Varsovie) to which I do not at present have access.
2. N. J. Lennes, Curves in non-metrical analysis situs with an application in the calculus of variations, American Journal of Mathematics33, (1911), S. 287?326.
3. A point is said to be a limit point of a point-setM if every circle which enclosesP encloses at least one point ofM distinct fromP.
4. Obviously every point-set which is connected in the strong sense is also connected in the weak sense and a closed point-set which is connected in the weak sense is also connected in the strong sense. It is accordingly allowable to speak of a ?closed, connected point-set? without specifying in which sense the term connected is used.
5. Cf Hans Hahn and S. Mazurkiewicz, loc. cit. Obviously every point-set which is connected in the strong sense is also connected in the weak sense and a closed point-set which is connected in the weak sense is also connected in the strong sense. It is accordingly allowable to speak of a ?closed, connected point-set? without specifying in which sense the term connected is used.