中文摘要：

设自然数n≥5,X_n={1,2,…,n},O_n是X_n上的保序变换半群,OCK_n是O_n中核具有连续横截面的元所构成的子半群,证明了K_r={α∈OCK_n：｜imα｜≤r}（1≤r≤n-1）的秩为（_r~n）.

英文摘要：

Let n≥5,X_n = {1,2,…,n},O_n be a semigroup of order-preserving transformations on X_n,OCK_nbe a subsemigroup consisting of a kernel with a continuous transversal in O_n,it was proved that the rank ofK_r = {α∈OCK_n：｜imα｜≤r}（1≤r≤n-1） is（_r~n）.