On initial and final fuzzy uniform structures

✍ Scribed by Fatma Bayoumi

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 235 KB
• Volume: 133
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(02)00329-9

✦ Synopsis

This paper is devoted to study the initial and ÿnal fuzzy uniform structures of the fuzzy uniform structure deÿned by the author and others in 1998. In this paper, we show that all initial and ÿnal lifts in the category FUN of these fuzzy uniform spaces and hence the initial and ÿnal fuzzy uniform structures exist. We introduce a characterization for the initial fuzzy uniform structures and as a special initial fuzzy uniform spaces the subspaces and product spaces of these fuzzy uniform spaces can be also characterized. We also show that the fuzzy topology (global homogeneous fuzzy neighborhood structure) associated to the initial fuzzy uniform structure of a family of fuzzy uniform structures coincides with the initial fuzzy topology (initial global homogeneous fuzzy neighborhood structure) of the family of fuzzy topologies (global homogeneous fuzzy neighborhood structures) associated to these fuzzy uniform structures.