点对称保序闭包函数的连续性和分离性
Continuity and separation for pointwise-symmetric isotonic closure functions
摘要：
在本文中，我们证明了一个逐点对称的保序闭包函数是由它所分离的集合对唯一确定的。然后，我们表明，当封闭功能的域是保序和封闭功能的codomain是保序和逐点对称，功能，分离只有那些对已经分离的集合是连续的。
英文摘要：
In this paper, we show that a pointwise-symmetric isotonic closure function is uniquely determined by the pairs of sets it separates. We then show that when the closure function of the domain is isotonic and the closure function of the codomain is isotonic and pointwise-symmetric, functions which separate only those pairs of sets which are already separated are continuous.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
