Approach theory in merotopic, Cauchy and convergence spaces. II (Q1307405)

The authors continue the study of Part I [ibid., 189-207 (1999; Zbl 0924.54013), see the review above]. They introduce the notion of approach-Cauchy structure and show that the category ACHY of approach-Cauchy spaces is a topological construct which is bireflectively embedded in AFIL. By strengthening the condition (ACHY) the authors define the concept of ultra approach-Cauchy structure and show that the category of ultra approach-Cauchy spaces is a Cartesian closed topological category which can be nicely embedded in the category ACHY.