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Ganguly, Dilip Kumar

Generalization of some known properties of Cantor set. (English) Zbl 0408.04001

Czech. Math. J. 28(103), 369-372 (1978).
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MSC:

03E15 Descriptive set theory

Keywords:

Cantor’s Ternary Set; Point of Trisection; Kinney’s Functions
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References:

[1] Bose Majumdar N. C.: On the distance set of the Cantor middle third set III. Amer. Math. Monthly 72 (1965), pp. 725-729. · Zbl 0154.05403 · doi:10.2307/2314413
[2] Dasgupta M.: On some properties of the Cantor set and the construction of a class of sets with Cantor set properties. Czechoslovak Mathematical Journal 24 (99), 1974 Praha, pp. 416-423. · Zbl 0309.28005
[3] Ganguly D. K., Bose Majumdar N. C: On some functions connected with Cantor set. Bull. Math, de la See. Sci. Math, de la R. S. R. · Zbl 0368.28001
[4] Kinney J. R.: A thin set of lines. Israel J. Math. 8 (1970), pp. 97- 102. · Zbl 0213.07605 · doi:10.1007/BF02771304
[5] Randolph J. F.: Distance between points of the Cantor set. Amer. Math. Monthly 47 (1940), pp. 549-551. · JFM 66.0203.02 · doi:10.2307/2303836
[6] Steinhaus H.: Nowa vlastnose mnogosci G. Cantora. Wektor (1917), pp. 105-107.
[7] Šalát T.: On the distance set of linear discontinuum I. (Russian), Časopis pro pěstování matematiky 87 (1962), pp. 4-16.
[8] Utz W. R.: The distance set for the Cantor discontinuum. Amer. Math. Monthly 58 (1951) pp. 407-408. · Zbl 0043.05402 · doi:10.2307/2306554
[9] Hobson E. W.: The theorey of function of a real variable and the theory of Fourier series. Vol. I, Dover Publications, Inc. p. 243.
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