Two meromorphic functions are said to share a set S ⊂ ℂ∪{∞} ignoring multiplicities (IM) if S has the same preimages under both functions. If any two nonconstant meromorphic functions sharing a set IM are identical, then the set is called a “reduced unique-range set for meromorphic functions” [RURSM (or URSM-IM)]. From the existing literature, it is known that there exists a RURSM with 17 elements. We reduce the cardinality of the existing RURSM and show that there exists a RURSM with 15 elements. Our result gives an affirmative answer to the question of L. Z. Yang [Int. Soc. Anal. Appl. Comput., 7, 551–564 (2000)].

如果S在两个函数下具有相同的原像，则称两个亚纯函数共享一个集合S ⊂ ℂ∪{∞} 忽略重数 (IM) 。如果共享一个集合 IM 的任何两个非常量亚纯函数是相同的，那么该集合被称为“亚纯函数的约简唯一范围集”[RURSM（或 URSM-IM）]。从现有文献可知，存在一个具有 17 个元素的 RURSM。我们减少了现有 RURSM 的基数，并表明存在一个具有 15 个元素的 RURSM。我们的结果对 LZ Yang [ Int. 社会。肛门。应用程序 计算。, 7, 551–564 (2000)]。