On local uniformities

✍ Scribed by J. Pelant; D. Preiss; J. Vilímovský

• Book ID: 103094098
• Publisher: Elsevier Science
• Year: 1978
• Weight: 644 KB
• Volume: 8
• Category: Article
• ISSN: 0016-660X
• DOI: 10.1016/0016-660x(78)90018-1

✦ Synopsis

Two concepts simplifying the inner structure of uniform spaces are examined, namely Ginsburg-Isbell concept of local fineness and that of functional lI>cal fm~~nessdue: to Z. FroKk (for definitions see below). It is shown that these two concepts are c:quivalent. Some information on Gir.?burg-Isbell derivatives of metric spaces and on the construction of locally fine coreflection is obtained. 0 I AMS Subj. Class.: Primary 54El5 functionally locally fine space stem of covers coreflective subcategory point-finite base . There are two definitions of local fineness in uniform spaces. The first one is the @ir?sburg-Isbell definition of locally fine spaces (LF), which are studieo in Isbell's book 121. ' This worlk was done: during the 2nd It;d nt .