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Journal : JURNAL DERIVAT: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA

Consistency Of Definition Of Orthogonality In A Partial Metric Induced By A Metric Mochammad Hafiizh; Nila Puspita Dewi; Sisworo; Dahliatul Hasanah
Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika Vol. 10 No. 1 (2023): Jurnal Derivat (April 2023)
Publisher : Pendidikan Matematika Universitas PGRI Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31316/jderivat.v10i1.4620

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
Co-Authors 'Azizah, Dewi Nur Abdur Rahman As’ari Agus Yulianto Amalia Martha Santosa Amanda Putri Enlisia Anas Ma’ruf Annizar Andrian Runtius Lalang Andrian Runtius Lalang Aulia Nadia Sari Barep Yohanes Bayu Nugroho Cholis Sa’dijah Dahliatul Hasanah Daiana, Putri Darmawan Satyananda Diyah Ayu Rizki Pradita Dwiyana Dwiyana Eddy Bambang Irawan Edy Bambang Irawan Erisca Lusy Rusdianti Erry Hidayanto Faradina, Erta Florianus Aloysius Nay Gatot Muhsetyo HAFIIZH, MOCHAMMAD Hasan Basri Hidayati, Vivi Rachmatul I Nengah Parta Ikhsana, Aulia Ilmiyatur Rosidah, Nilta Indah Puspitasari Maharani Indayani, Nunik Ipung Yuwono, Ipung Izzah, Nuurul Kamirsyah Wahyu Laily Wijayanti Utami Lathiful Anwar Lela Nur Safrida Mahmuddin Yunus Maimunah Maimunah Maimunah, Maimunah Mariana, Erna Mei Radia Putri Mirza Amelia Oktaviani Mohammad Akbar Muazarah, Salma Farihah Muhammad Irfan Nadia Nurudini Naela Nur Azizah Niila Amaalia Chasanah Nila Puspita Dewi Nilta Ilmiyatur Rosidah Nugraheni, Dinda Dwi Nugroho, Herlambang Tri Nunik Indayani Parta, I Negah Patma Sopamena Permadi, Hendro Purwanto Purwanto Purwanto Purwanto Purwanto Purwanto Putra, Zuhadur Ra'is Ariyono Qohar, Abd. Raey Hanah Rani Martalisa Taorina Refni Adesia Pradiarti Rifaatul Mahmudah Rustanto Rahardi Safitri, Rizqi Febriana Sartati, Setiawan Budi SATRIYAS ILYAS Setiawan Budi Sartati Shofi Farihah Muazarah Subanji Subanji Suci Zuhriati Sudirman Sudirman Sudirman Sudirman Susiswo Swalaganata, Galandaru Swasono Rahardjo Tasni, Nurfaida Tiwi Nur Masita Tjang Daniel Chandra Toto Nusantara Ulfa Rahmawati Untu, Zainuddin Untu Wasti Tampi Wasti Tampi Yandi Raharjo, Eko Yayan Eryk Setiawan Yudha, Sri Indah Dwirahmasari Zuhadur Ra'is Ariyono Putra