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A convex metric for a locally connected continuum. (English) Zbl 0035.10801


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[1] Gustav Beer, Beweis des Satzes, dass jede im kleinen zusammenhängende Kurve konvex metrisiert werden kann, Fund. Math. vol. 31 (1938) pp. 281-320. · Zbl 0020.40402
[2] R. H. Bing, Extending a metric, Duke Math. J. 14 (1947), 511 – 519. · Zbl 0030.08003
[3] Orville G. Harrold Jr., Concerning the Convexification of Continuous Curves, Amer. J. Math. 61 (1939), no. 1, 210 – 216. · Zbl 0020.07601 · doi:10.2307/2371400
[4] C. Kuratowski and G. T. Whyburn, Sur les éléments cycliques et leurs applications, Fund. Math. vol. 16 (1930) pp. 305-331.
[5] Karl Menger, Untersuchungen über allgemeine Metrik, Math. Ann. 100 (1928), no. 1, 75 – 163 (German). · doi:10.1007/BF01448840
[6] R. L. Wilder, On the imbedding of subsets of a metric space in Jordan continua, Fund. Math. vol. 19 (1932) pp. 45-64. · Zbl 0005.18302
[7] Leo Zippin, A study of continuous curves and their relation to the Janiszewski-Mullikin theorem, Trans. Amer. Math. Soc. 31 (1929), no. 4, 744 – 770.
[8] Edwin E. Moise, Grille decomposition and convexification theorems for compact metric locally connected continua, Bull. Amer. Math. Soc. 55 (1949), 1111 – 1121. · Zbl 0036.11801
[9] R. H. Bing, Partitioning a set, Bull. Amer. Math. Soc. 55 (1949), 1101 – 1110. · Zbl 0036.11702
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