On Generalized Injective Spaces in Generalized Topologies
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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.
کلید واژگان
generalized continuitygeneralized embedding
generalized dual-injective space
Császár product
شماره نشریه
12تاریخ نشر
2018-01-011396-10-11
ناشر
Science and Research Branch, Islamic Azad Universityدانشگاه آزاد اسلامی واحد علوم و تحقیقات
