The midpoint set of a cantor set
A non-endpoint of the Cantor ternary set is any Cantor point which is not an endpoint of one of the remaining closed intervals obtained in the usual construction process of the Cantor ternary set in the unit interval. It is shown that the set of points in the unit interval which are not midway betwe...
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| Format: | Article |
| Language: | English |
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Wiley
1978-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117127800054X |
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| _version_ | 1849521464656527360 |
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| author | Ken W. Lee |
| author_facet | Ken W. Lee |
| author_sort | Ken W. Lee |
| collection | DOAJ |
| description | A non-endpoint of the Cantor ternary set is any Cantor point which is not an endpoint of one of the remaining closed intervals obtained in the usual construction process of the Cantor ternary set in the unit interval. It is shown that the set of points in the unit interval which are not midway between two distinct Cantor ternary points is precisely the set of Cantor nonendpoints. It is also shown that the generalized Cantor set Cλ, for 1/3<λ<1, has void intersection with its set of midpoints obtained from distinct members of Cλ. |
| format | Article |
| id | doaj-art-fe11541ebb1a4ecfa19b32fbb395f0c5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1978-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fe11541ebb1a4ecfa19b32fbb395f0c52025-08-20T03:25:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251978-01-011454154610.1155/S016117127800054XThe midpoint set of a cantor setKen W. Lee0Department of Mathematical Sciences, Missouri Western State College, 4525 Downs Drive, Saint Joseph 64507, Missouri, USAA non-endpoint of the Cantor ternary set is any Cantor point which is not an endpoint of one of the remaining closed intervals obtained in the usual construction process of the Cantor ternary set in the unit interval. It is shown that the set of points in the unit interval which are not midway between two distinct Cantor ternary points is precisely the set of Cantor nonendpoints. It is also shown that the generalized Cantor set Cλ, for 1/3<λ<1, has void intersection with its set of midpoints obtained from distinct members of Cλ.http://dx.doi.org/10.1155/S016117127800054Xcantor setmidpoint setdistance set. |
| spellingShingle | Ken W. Lee The midpoint set of a cantor set International Journal of Mathematics and Mathematical Sciences cantor set midpoint set distance set. |
| title | The midpoint set of a cantor set |
| title_full | The midpoint set of a cantor set |
| title_fullStr | The midpoint set of a cantor set |
| title_full_unstemmed | The midpoint set of a cantor set |
| title_short | The midpoint set of a cantor set |
| title_sort | midpoint set of a cantor set |
| topic | cantor set midpoint set distance set. |
| url | http://dx.doi.org/10.1155/S016117127800054X |
| work_keys_str_mv | AT kenwlee themidpointsetofacantorset AT kenwlee midpointsetofacantorset |