On Product Stable Quotient Order-homomorphisms

Document Type : Research Paper

Authors

1 Department of mathematices, sirjan university of technology

2 1Department of Mathematics, University of Hormozgan, Bandarabbas, Iran

10.22103/jmmrc.2021.14803.1103

Abstract

In this paper, we study the properties of some classes of quotient
order-homomorphisms, as product stable in the category of topological fuzzes.
We de ne the concept of a bi-quotient order-homomorphism and show that for
Hausdorff topological fuzzes, a quotient order-homomorphism f : L1 ! L2 is
product stable if and only if f is bi-quotient and L2 is a core compact topological
fuzz.

Keywords


[1] J. Adamek, H. Herrlich and G.E. Strecker, Abstract and concrete categories, John Wiley
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] S.Z. Bai, Q-convergence of ideals in fuzzy lattices and its applications, Fuzzy Sets and
Systems, 92 (1997), 357{363.
[4] C.L. Chang, Fuzzy topology spaces, J. Math. Anal. Appl., 24 (1968), 182{190.
[5] Y. Chen, Convergence in topological molecular lattices, Fuzzy Sets and Systems, 84
(1996), 97{102.
[6] S.L. Chen and Z.X. Wu, Urysohn separation property in topological molecular lattices,
Fuzzy Sets and Systems, 123 (2001), 177{184.
[7] B.J. Day and G.M. Kelly, On topological quotient maps preserved by pullback or prod-
ucts, Proc. Cambridge Phil. Soc., 67 (1970), 553{558.
[8] M. Demirci, Category theoretic fuzzy topological spaces and their dualities, Fuzzy Sets
and Systems, 227 (2013), 1{24.
[9] K. El-Saady and F. Al-Nabbat, Generalized topological molecular lattices, Advances in
Pure Mathematics, 5 (2015), 552{559.
[10] K. El-Saady and A. Ghareeb, Net-convergence and weak separation axioms in (L;M)-
fuzzy topological molecular lattices, J. Egyptian Math. Soc., 21 (2013), 305{310.
[11] MH. Escardo and R. Heckmann, Topologies on spaces of continuous functions, Topology
Proceedings, 26 (2001-2002), 545{565.
[12] B. Hutton, Product of fuzzy topological spaces, Topology Appl., 11 (1980), 59{67.
[13] B. Hutton and I. Reilly, Separation axioms in fuzzy topological spaces , Fuzzy Sets and
Systems, 3 (1980), 93{104.
[14] Y.M. Li, Exponentiable objects in the category of topological molecular lattices, Fuzzy
Sets and Systems, 104 (1999), 407{414.
[15] Y.M. Li and Z.H. Li, Top is a re
ective and core
ective subcategory of fuzzy topological
spaces, Fuzzy Sets and Systems, 116 (2000), 429{432.
[16] Y.M. Li and G.J. Wang, Re
ectiveness and core
ectiveness between the category of
topological spaces, the category of fuzzy topological spaces and the category of topological
molecular lattices, Acta Math. Sinica, 41(4) (1998), 731{736.
[17] E. Michael, Bi-quotient maps and cartesian products of quotient maps, Annales de L,
institute Fourier, 18 (1968), 287{302.
[18] Gh. Mirhosseinkhani, Relative compactness and product stable quotient maps, Bull. Ira-
nian Math., 36 (2010), 93{101.
[19] Gh. Mirhosseinkhani, On product stable quotient maps, Algebras Groups and Geome-
tries, 25 (2008), 343{352.
[20] N. Nazari and GH. Mirhosseinkhani, On generalized topological molecular lattices, Sa-
hand Communications in Mathematical Analysis, 10(1) (2018), 1{15.
[21] G.J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47 (1992),
351{376.
[22] G.J. Wang, Order-homomorphisms on fuzzes, Fuzzy Sets and Systems, 12 (1984), 281{
288.
[23] Z. Yang, The cartesian closedness of the category Fuzz and function spaces on topological
fuzzes, Fuzzy Sets and Systems, 61 (1994), 341{351.