On Generalized Injective Spaces in Generalized Topologies
Subject Areas : Statistics
1 - Department of Mathematics, Tafresh University, Tafresh, Iran
Keywords: پیوستگی تعمیم یافته, نشاننده تعمیم یافته, فضای انژکتیو- چگال تعمیم یافته, حاصلضرب سازار,
Abstract :
In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, introducing the concept of the generalized embedding and the generalized injection, we study Császár product of generalized spaces in the category of generalized topological spaces. Using by the tools of category theory, we describe the results of classifying on the generalized injective spaces in which these spaces are characterized as generalized embedding of Császár product with the product topology of two points Sierpinski space. Finally, the generalized dual-injection spaces as the objects of a special subcategory of the generalized topological spaces are studied for which all single-point subsets are closed.
[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, John Wiley and sons,Inc., 1990.
[2] E. 1ech, Topological spaces, Publishing House of Czechoslovak Acad. Sci., Wiley, London, 1966.
[3] Á. Császár, Foundations of General Topology, Pergamon Press, London, 1963.
[4] Á. Császár, Generalized open sets, Acta Math. Hungar., 75 (1997), 65-87.
[5] Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), 351-357.
[6] Á. Császár, Generalized open sets in generalized topologies, Acta Math. Hungar., 106 (1-2) (2005), 53-66.
[7] Á. Császár, Monotonicity properties of operations on generalized topologies, Acta Math. Hungar., 108 (4) (2005), 351-354.
[8] Á. Császár, Product of generalized topologies}, Acta Math. Hungar., 123 (1-2) (2009), 127-132.
[9] E. Makai Jr., E. Peyghan and B. Samadi, Weak and strong structures and the T_3.5 property for generalized topological spaces, Acta Math. Hungar., 150 (1) (2016), 1-35.
[10] L. E. Saraiva, Generalized quotient topologies, Acta Math. Hungar., 132 (1-2) (2011), 168-173.
[11] D. S. Scott, Continuous lattice, Lecture Notes in Math., Springer, Berlin, 274 (1972), 97-137.
