- 期刊
THE MIDPOINT SET OF A CANTOR SET
並列摘要
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 preclsely the set of Cantor non-endpoints. It is also shown that the generalized Cantor set C_λ, for 1/3＜λ＜1, has void intersection with its set of midpoints obtained from distinct members of C_λ.