Approach Spaces, Limit Tower Spaces, and Probabilistic Convergence Spaces

Applied Categorical Structures

Volumn 5, Issue 2, 1997, Pages 99-110

  Brock, Paul ^a   Kent, D C ^a  

^a WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

Approach space; Convergence approach limit; Isomorphism functor; Limit tower; Probabilistic convergence space; t norm

Indexed keywords

EID: 0002326825     PISSN: 09272852     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008633124960     Document Type: Article

References (13)

1. Cook, C. H. and Fischer, H. R.: Regular convergence spaces, Math Ann. 174 (1967), 1-7.
2. Florescu, L.C.: Probabilistic convergence structures, Aequationes Math. 38 (1989), 123-145.
3. Frank, M. J.: Probabilistic topological spaces, J. Math. Analysis and Appl. 34 (1971), 67-81.
4. Kowalsky, H. J.: Limesräume und Komplettierung, Math. Nachr. 12 (1954), 301-340.
5. Lowen, E. and Lowen, R.: A quasi topos containing CONV and MET as full subcategories, Intl. J. Math. Math. Sci. 11 (1988) 417-438.
6. Lowen, E. and Lowen, R.: Topological quasi-topos hulls of categories containing topological and metric objects, Cahiers Top. Geom. Diff. 30 (1989), 213-228.
7. Lowen, R.: Approach spaces: A common supercategory of Top and Met, Math. Nachr. 141 (1989), 183-226.
8. Lowen, R.: Approach Spaces, Oxford Mathematical Monographs, Oxford University Press, 1996.
9. Menger, K.: Statistical metrics, Proc. Natl. Acad. Sci. USA 37 (1951), 178-180.
10. Preuss, G.: Theory of Topological Structures (Kluwer Academic Publishers, 1987).
11. Richardson, G. D. and Kent, D. C.: Probabilistic Convergence Spaces, J. Austral. Math. Soc. 61 (1996), 1-21.
12. Schweizer, B. and Sklar, A.: Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334.
13. Schweizer, B. and Sklar, A.: Probabilistic Metric Spaces, North-Holland Publ. Co., New York, 1983.