Proyecciones Journal of Mathematics
Vol. 28, N° 2, pp. 181-201, August 2009.
Universidad Católica del Norte
Antofagasta - Chile


PRODUCTS OF LF-TOPOLOGIES AND SEPARATION IN LF-TOP


Carlos Orlando Ochoa C¹
Joaquín Luna - Torres²

¹Univ. Distrital Francisco José De Caldas, Colombia
²Universidad De Cartagena, Colombia


Correspondencia a:

---

Abstract

For a GL-monoid L provided with an uniform structure, we build an LF-topology on the cartesian product of a family of LF-topological spaces. We also show that the product of an arbitrary family of Kolmogoroff (Hausdorff) LF-topological spaces is again a Kolmogoroff (Hausdorff) LF-topological space.

Subjclass[2000]: 54A4O, 54B10, 06D72

Keywords : Topological spaces, Uniform Spaces, GL-monoids, LF-topological spaces, Cartesian product, Kolmogoroff Space, Hausdorff Space

---

References

[1] Jiri Adamek, Horst Herrlich, George Strecker, Abstract and Concrete Categories, John Wiley & Sons, New York, (1990).

[2] G. Birkhoff, Lattice Theory, American Mathematical Society, Providence, (1940).

[3] N. Bourbaki, General Topology, Addison-Wesley Publishing, Massachusetts, (1966).

[4] U. Höhle, A. Šostak, Fixed-Basis Fuzzy Topologies la: Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, Kluwer Academic Publisher, Boston, (1999).

[5] P. T. Johnstone, Stone spaces, Cambridge University Press, Cambridge, (1982).

[6] W. Kotzé, Uniform, Spaces In: Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, Kluwer Academic Publisher, Boston, (1999).

[7] Liu Ying-Ming, Luo Mao-Kang, Fuzzy Topology, World Scientific, Singapore, (1997).

[8] S. E. Rodabaugh, Power set Operator Foundations For Poslat Fuzzy Set Theories and Topologies, In: Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, Kluwer Academic Publisher, Boston, (1999).

[9] A P. Sostak, Fuzzy functions and an extension of the category L-Top of Chang-Goguen L-topological spaces, Proceedings of the Ninth Prague Topological Symposium, Prague, Czech Republic, (2001).

[10] S. Willard, General Topology, Addison-Wesley Publishing Company, Massachusetts, (1970).

[11] Yueli Yue, Jinming Fang, On Separation axioms in I-fuzzy topological spaces, Fuzzy sets and systems, Elsevier, (2005).

 

Carlos Orlando Ochoa C.
Proyecto Curricular de Matemáticas
Facultad de Ciencias y Educación
Universidad Distrital Francisco José de Caldas
Colombia
e-mail : oochoac@udistrital.edu.co camicy@etb.net.co

Joaquín Luna-Torres
Departamento de Matemáticas
Universidad de Cartagena
Bogotá
Colombia
e-mail : jlunator@gmail.com

---

Received : October 2008. Accepted : June 2009