A Short Note on the Role of Grills in Nearness Frames FULL TEXT

Year 2012, Volume: 41 Issue: 1, 85 - 91, 01.01.2012

Martin M. Mugochi

Keywords

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References

• Banaschewski, B. Uniform completion in pointfree topology (Topological and algebraic struc- tures in fuzzy sets 19–56, Trends Log. Stud. Log. Libr., 20, Kluwer Acad. Publ., Dordrecht, 2003). [2] Banaschewski, B., Hong, S. S. and Pultr, A. On the completion of nearness frames, Quaest. Math. 28, 19–37, 1998.
• Banaschewski, B. and Pultr, A. Cauchy points of uniform and nearness frames, Quaest. Math. 19, 107–127, 1996.
• Bentley, H. L. and Herrlich, H. Extensions of topological spaces, In: Topology, Proceedings of the Memphis State University Conference, 1975, Ed.: S.P. Franklin and B.V. Smith-Thomas, Marcel Dekker, New York, 129–184, 1976.
• Choquet, G. Sur les notions de filtre et de grille, Comptes Rendus Acad. Sci. Paris 224, 171–173, 1947.
• Dube, T. Structures in frames (PhD Thesis, University of Durban-Westville, 1992).
• Gratzer, G. Lattice Theory: First concepts and distributive lattices (W. H. Freeman and Co., San Fransisco, Carlifornia, 1971).
• Herrlich, H. Topological structures, Topological Structures 1, Math. Centre Tracts, 59–122, 1974. [9] Johnstone, P. T. Stone Spaces (Cambridge Univ. Press, Cambridge, 1982).
• Mugochi, M. M. Contributions to the theory of nearness in pointfree topology (PhD Thesis, University of South Africa, 2009).
• Preuss, G. Theory of topological structures: An approach to categorical topology (D. Reidel Pub Co., 1987).
• Thron, W. J. Proximity structures and grills, Math. Ann. 206, 35–62, 1973.