| Title:
|
On some properties of the Cantor set and the construction of a class of sets with Cantor set properties (English) |
| Author:
|
Dasgupta, Maitreyee |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
24 |
| Issue:
|
3 |
| Year:
|
1974 |
| Pages:
|
416-423 |
| . |
| Category:
|
math |
| . |
| MSC:
|
04A15 |
| idZBL:
|
Zbl 0309.28005 |
| idMR:
|
MR0366673 |
| DOI:
|
10.21136/CMJ.1974.101256 |
| . |
| Date available:
|
2008-06-09T14:08:04Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101256 |
| . |
| Reference:
|
[1] Boas R. P., Jr.: The distance set of the Cantor set.Bull. Cal. Math. Soc., 54 (1962), p. 103. Zbl 0112.28602, MR 0170820 |
| Reference:
|
[2] Bose Majumder N. C.: On the distance set of the Cantor middle third set.Bull. Cal. Math. Soc., 51 (1959), p. 93. MR 0112113 |
| Reference:
|
[3] Bose Majumder N. C.: A Study of certain properties of the Cantor set and of an SD-set.Bull. Cal. Math. Soc., 54, 1, March (1962), p. 8. Zbl 0114.38603, MR 0167950 |
| Reference:
|
[4] Bose Majumder N. C.: On the distance set of the Cantor middle third set.III, Amer. Math. Monthly, 72 (1965), p. 725. Zbl 0154.05403, MR 0183819, 10.1080/00029890.1965.11970598 |
| Reference:
|
[5] Erdös P., Kakutani S.: On a perfect set.Coll. Math., IV, 2 (1957). MR 0089886 |
| Reference:
|
[6] Kinney J. R.: A thin set of lines.Israel J. Math., 8 (1970), p. 97. Zbl 0213.07605, MR 0265534, 10.1007/BF02771304 |
| Reference:
|
[7] Marczewski E.: .Coll. Math., (1955), p. 125. Zbl 0066.29901 |
| Reference:
|
[8] Randolph J. F.: Distances between points of the Cantor set.Amer. Math. Monthly, 47 (1940), p. 549. MR 1524942, 10.2307/2303836 |
| Reference:
|
[9] Randolph J. F.: Real and abstract analysis.Academic Press, N. Y. (1968), p. 101. Zbl 0165.37201, MR 0225618 |
| Reference:
|
[10] Šalát T.: On the distance set of linear discontinuum I.(Russian), Časopis pro pěstování matematiky, 87 (1962), p. 4. MR 0180959 |
| Reference:
|
[11] Sierpiński W.: On the congruence of sets and their equivalence by finite decomposition.Lucknow University Studies (1954). MR 0060567 |
| Reference:
|
[12] Steinhaus H.: Nowa vlastnośc mnogości G. Cantora.Wektor (1917), p. 105. |
| Reference:
|
[13] Steinhaus H.: Sur les distances des points des ensembles de mesure positive.Fundam. Math., 1 (1920), p. 93. MR 0065059, 10.4064/fm-1-1-93-104 |
| Reference:
|
[14] Utz W. R.: The distance set for the Cantor discontinuum.Amer. Math. Monthly, 58 (1951), p. 407. Zbl 0043.05402, MR 1527894, 10.2307/2306554 |
| . |
