Himpunan Buka Infra, Interior Infra, dan Himpunan i-Genuine - Ismail, Nurus Shubhiyyah; Maharani, Dian (Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang, 2024)
This research examines the properties of infra open set and infra interior in infra topological space. Unlike ordinary topology, infra topology has a unique characteristic where the union of any collection of its members is not necessarily an infra topology. This leads to differences in the properties of infra open sets and infra interiors compared to open sets and interiors in ordinary topology. The main objective of this research is to prove the properties of infra open sets and infra interiors on infra topological spaces. In addition, this research also includes the prove of basic properties of other concepts in infra topology, such as the i-genuine set. The results show that the interior infra of A⊆X is the largest open infra set contained in A on the infra topological space (X,τ_iX) if A is an i-genuine set. Moreover, it is found that if A∈τ_iX, then iInt(A)∈τ_iX and iInt(A)=A, iInt(A∩B)=iInt(A)∩iInt(B), every singleton is an i-genuine set, and if iInt(A)=A, then A is either an infra-open set or not. This research also discusses the relationship between i-genuine and non-i-genuine sets in infra topological space related to their union and intersection. This research is expected to provide benefits and become an additional reference for further research related to the set of open infra and interior infra.