一致空间与连续空间
Uniformites et Continuity Spaces
摘要：
半群A是单位元为0的阿贝尔半群。A中的一个正集是一个有序的下有向集P，其中每个r都包含一个元素r/2，r/2 + r/2 = r。连续空间是一个抽象集合X，其上有一个映射d：XxX到A，满足d（x，x）= 0和d（x，z）d（x，y）+ d（y，z）。一个拟一致空间是一个抽象集合X，它配备了一个二元关系{U}的滤子基，使得每个U都包含对角线，并且对于某些V{U}。对于每个rP，可以看到集合}是X上的准均匀滤子基。实际上，P的向下方向性确保U（r）是对角线的覆盖的滤子基，并且U（r）包含U（r/2）U（r/2）。通过对称化，即通过将U（r）与U（s）= {（y，x）|d（y，x）<s}。
英文摘要：
A semigroup A is an abelian semigroup with identity 0. A set of positives in A is an ordered down-directed set P containing with every r an element r/2 with r/2 + r/2 = r. A continuity space is an abstract set X equipped with a map d : XxX to A satisfying d(x, x) = 0 and d(x, z) d(x, y) + d(y, z). A quasi-uniform space is an abstract set X equipped with a filterbase of binary relations {U} such that each U contains the diagonal as well as for some V{U}. For each rP, the set } is seen to be a quasi-uniform filterbase on X . Indeed, the down-directedness of P ensures that U(r) is a filterbase of oversets of the diagonal and U(r) contains U(r/2)U(r/2). One obtains a uniform filterbase by symmetrization, i.e. by intersecting the U(r) with the U(s) = {(y, x)|d(y, x) <s}.
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。
