关于Artico-Moresco fuzzy近性空间的一点注记(英文)

A Note on Artico-Moresco Fuzzy Proximity Spaces

最近 ,张德学引入了拓扑构造的co tower扩张的概念 ,并证明了fuzzy拓扑学中出现的一些熟知的范畴可以表示为较为简单的范畴的co tower扩张 .作者证明了由G .Artico与R .Moresco引入的fuzzy近性空间范畴FPS具体同构于近性空间范畴PROX的co tower扩张 .注意到由R .Lowen引入的fuzzy一致空间范畴FUS是一致空间范畴UNIF的co tower扩张 ,这一结论解释了为何FPS与FUS是相容的 .另外 ,作者还指出由G .Artico与R .Moresco引入的FUS与FPS之间的两个函子也是其经典情形的co tower扩张 .

Zhang introduced a construction called the co tower extension of topological constructs, and proved that several familiar constructs in fuzzy topology can be expressed as co tower extension of simpler constructs. In this note, it is proved that the construct of fuzzy proximity spaces FPS introduced by G.Artico and R.Moresco is concretely isomorphic to the co tower extension of PROX, the construct of proximity spaces. Note that the construct FUS introduced by R. Lowen, which, again, is the co tower extension of the construct of uniform spaces, this explains why FPS is compatible with FUS. The authors also show that the two functors between FUS andFPS introduced by G.Artico and R.Moresco are also the co tower extension of their canonical counterparts.