JURNAL DERIVAT: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA
Vol. 10 No. 1 (2023): Jurnal Derivat (April 2023)

Consistency Of Definition Of Orthogonality In A Partial Metric Induced By A Metric

Mochammad Hafiizh (Mathematics Departmen, Universitas Negeri Malang)
Nila Puspita Dewi (Mathematics Department, Universitas Negeri Malang)
Sisworo (Mathematics Departmen, Universitas Negeri Malang)
Dahliatul Hasanah (Mathematics Department, Universitas Negeri Malang)



Article Info

Publish Date
30 Apr 2023

Abstract

An extension of the metric space in which the distance of the same point is not always zero is called a partial metric space. Orthogonality is the relation of two perpendicular lines at one point of intersection forming a right angle. There are several ways to define orthogonality, including Pythagorean Orthogonality, Isosceles Orthogonality, and Birkhoff-James Orthogonality. The purpose of this research is to study the consistency of the definition of orthogonality in the metric space to the partial metric space. Based on these results, it can be concluded that the partial metric space can be obtained by linear induction from a metric space. Then, in developing the definition of orthogonality to the partial metric space, it can be concluded that the qualified orthogonality is the I-orthogonality and the BJ-orthogonality, while the P-orthogonality does not qualify the consistency of the definition of orthogonality in the partial metric space. Kata Kunci: Orthogonality, Consistency, and Partial metric space

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Journal Info

Abbrev

derivat

Publisher

Subject

Education

Description

Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika, e-ISSN: 2549-2616, p-ISSN: 2407-3792 Is an information container containing scientific articles of research, literature studies, ideas, the application of theory, the study of critical analysis, and Islamic studies in the field mathematics ...