ON GENERALIZED INJECTIVE SPACES IN GENERALIZED TOPOLOGIES

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ARIANPOOR H.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2018 | Volume:3 | Issue:12 Page(s): 15-24

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Title

ON GENERALIZED INJECTIVE SPACES IN GENERALIZED TOPOLOGIES

Author(s)

ARIANPOOR H. | Issue Writer Certificate

Keywords

GENERALIZED CONTINUITYQ1

GENERALIZED EMBEDDINGQ1

GENERALIZED DUALINJECTIVE SPACEQ1

CSÁSZÁR PRODUCTQ1

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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APA: Copy

ARIANPOOR, H.. (2018). ON GENERALIZED INJECTIVE SPACES IN GENERALIZED TOPOLOGIES. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 3(12 ), 15-24. SID. https://sid.ir/paper/257364/en

Vancouver: Copy

ARIANPOOR H.. ON GENERALIZED INJECTIVE SPACES IN GENERALIZED TOPOLOGIES. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2018;3(12 ):15-24. Available from: https://sid.ir/paper/257364/en

IEEE: Copy

H. ARIANPOOR, “ON GENERALIZED INJECTIVE SPACES IN GENERALIZED TOPOLOGIES,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 3, no. 12 , pp. 15–24, 2018, [Online]. Available: https://sid.ir/paper/257364/en

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