A fuzzy modification of the category of linearly ordered spaces. (English) Zbl 0594.54003

Shostak, A.

Commentat. Math. Univ. Carol. 26, 421-442 (1985).

The author has previously studied [in Topology theory and applications, 5th Colloq., Eger/Hung. 1983, Colloq. Math. Soc. János Bolyai 41, 581- 604 (1985)] a generalization of B. Hutton’s fuzzy unit interval [J. Math. Anal. Appl. 50, 74-79 (1975; Zbl 0297.54003)]. He extends his construction to yield a faithful (or embedding) functor from the category of linearly ordered spaces with increasing continuous mappings into the category of Lowen-type fuzzy topological spaces. He also proves that for connected linearly ordered spaces his construction is equivalent to one proposed by the reviewer [Fuzzy Sets Syst. 12, 271-279 (1984; Zbl 0549.54004)].

Reviewer: A.J.Klein

MSC:

54A40	Fuzzy topology
54B30	Categorical methods in general topology
54F05	Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

Keywords:

fuzzy unit interval; category of linearly ordered spaces; category of Lowen-type fuzzy topological spaces

Citations:

Zbl 0297.54003; Zbl 0549.54004