نوع مقاله : مقاله پژوهشی
نویسندگان
1 گروه ریاضی، دانشکده ریاضی و علوم کامپیوتر، دانشگاه صنعتی سیرجان، سیرجان، ایران
2 دانشگاه پیام نور
چکیده
کلیدواژهها
موضوعات
عنوان مقاله [English]
نویسندگان [English]
In this paper, we study the categorical structures of the concepts of ideal, grill, primal, and filter, which play a fundamental and important role in the study of topology spaces. Some researchers have shown that all these concepts are equivalent, regardless of the categorical viewpoint. Here, we define the homomorphisms and so the category of each of these concepts and then show that all of them are isomorphic, except for the category of filters. As an important result, it has been shown that these categories are topological, except for the category of filters. Consequently, they are complete and cocomplete, but they are not algebraic. Thus, many topological properties can be easily expressed and analyzed in terms of each of these concepts. Finally, some categorical structures of ideals are described.
کلیدواژهها [English]
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