文章基本信息

标题：The midpoint set of a cantor set
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作者：Ken W. Lee
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1978
卷号：1
DOI：10.1155/S016117127800054X
出版社：Hindawi Publishing Corporation
摘要：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.