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Information Journal Paper

Title

ON GENERALIZED INJECTIVE SPACES IN GENERALIZED TOPOLOGIES

Writers

ARIANPOOR H.

Pages

 Start Page 15 | End Page 24

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 singlepoint subsets are closed.

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