INTERIOR DAN CLOSURE PADA RUANG TOPOLOGI CENTRAL

UTAMA, ILHAM INDRA and Dewi, Novi Rustiana and Cahyono, Endro Setyo (2025) INTERIOR DAN CLOSURE PADA RUANG TOPOLOGI CENTRAL. Undergraduate thesis, Sriwijaya University.

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Abstract

The generalization of the definition of topological space is not a new discovery. For example, supra topological space which reduces the axiom that the intersection of topological members is also a topological member and infra topological space which reduces the axiom that the union of topological members is also a topological member. In this research, a new topology is formed by reducing the axioms of one topology about ∅ and X which are members of the topology and called the central topology. ∅ and X that are no longer members of the topology cause some changes in the properties of the sets in it, especially in the interior and closure of a set. The purpose of this research is to define the central topology and study the properties that change because ∅ and X are no longer members of the topology. The result obtained from this research is the existence of sets that have neither interior nor closure. The set that still has interior is called ic-exist set while the set that has ∅ as interior loses its interior and is called non ic-exist set. The set that still has a closure is called a cc-exist set while the set that has X as a closure loses its closure and is called a non-cc-exist set. The ic-exist and cc-exist sets retain their properties even when operated on by the intersection or union of two neighboring sets while the non ic-exist set may form an ic-exist set if a union between two non ic-exist sets is performed and the non cc-exist set may form a cc-exist set if a union between two non cc-exist sets is performed.

Item Type:	Thesis (Undergraduate)
Subjects:	Q Science > QA Mathematics > QA1-43 General
Divisions:	08-Faculty of Mathematics and Natural Science > 44201-Mathematics (S1)
Depositing User:	ILHAM INDRA UTAMA
Date Deposited:	14 Jul 2025 07:53
Last Modified:	14 Jul 2025 07:53
URI:	http://repository.unsri.ac.id/id/eprint/178341

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