Cartesian closed subcategories of topological fuzzes

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Hormozgan, Bandarabbas, Iran

2 Department of mathematics and Computer Sciences, Sirjan University of Technology, Sirjan, Iran.

10.29252/as.2019.1335

Abstract

A category $\mathbf{C}$ is called Cartesian closed  provided that it has finite products and for each
$\mathbf{C}$-object $A$ the functor $(A\times -): A\ra A$ has a right adjoint. It is well known that the category $\mathbf{TopFuzz}$  of all topological fuzzes is both complete  and cocomplete, but it is not Cartesian closed. In this paper, we introduce some Cartesian closed subcategories of this category.

Keywords


[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, John Wiely and Sons Inc., New York, 1990.
[2] M. Akbarpour and GH. Mirhosseinkhani, Exponentiable objects in some categories of topological molecular lattices, Hadronic Journal, 40 (2017), 327-344.
[3] M. Escardo, J. Lawson and A. Simpson, Comparing cartesian closed categories of (core)compactly generated spaces, Topology Appl., 143 (2004), 105-145.
[4] B. Hutton, Products of fuzzy topological spaces, Topology Appl., 11 (1980), 59-67.
[5] B. Hutton and I. Reilly, Separation axioms in fuzzy topological spaces, Fuzzy Sets and Systems, 3 (1980), 93-104.
[6] Y.M. Li, Exponentiable objects in the category of topological molecular lattices, Fuzzy Sets and Systems, 104 (1999), 407-414.
[7] Y.M. Li, Generalized (S,I)-complete free completely distributive lattices generated by posets, Semigroup Forum, 57 (1998), 240-248.
[8] Y.M. Li and Z.H. Li, Top is a reective and coreective subcategory of fuzzy topological spaces, Fuzzy Sets and Systems, 116 (2000), 429-432.
[9] G.J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47 (1992), 351-376.
[10] G.J. Wang, Order-homomorphisms on fuzzes, Fuzzy Sets and Systems, 12 (1984), 281-288.
[11] Z. Yang, The cartesian closedness of the category Fuzz and function spaces on topological
fuzzes, Fuzzy Sets and Systems, 61 (1994), 341-351.