Monadic convergence structures. (English) Zbl 1041.54007
Rodabaugh, Stephen Ernest (ed.) et al., Topological and algebraic structures in fuzzy sets. A handbook of recent developments in the mathematics of fuzzy sets. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1515-1/hbk). Trends Log. Stud. Log. Libr. 20, 57-79 (2003).
The author summarizes results on partially ordered monads to get a unifying theory of monadic convergence including probabilistic convergence, limit towers and graded fuzzy convergence. He gives characterisations of (extended) fuzzy pretopologies by their interior operators, of the neighbourhood operator by sup-inverses, of monadic topologies by a diagonal axiom and of regularity by the closure operator. Further, separation axioms up to normality are studied.
For the entire collection see [Zbl 1020.00006].
For the entire collection see [Zbl 1020.00006].
Reviewer: Bernhard Behrens (Göteborg)
MSC:
| 54A40 | Fuzzy topology |
| 54A05 | Topological spaces and generalizations (closure spaces, etc.) |
| 54A20 | Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) |
| 18C15 | Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads |
| 54D10 | Lower separation axioms (\(T_0\)–\(T_3\), etc.) |
| 54D15 | Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) |
