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.

Abstract

A category C is called Cartesian closed  provided that it has finite products and for each
C-object A the functor (A×−):A\raA has a right adjoint. It is well known that the category 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

References

[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.
Algebraic Structures and Their Applications
Volume 6, Issue 1
March 2019
Pages 23-33

Files

Share

How to cite

Statistics