The answer is support system.
A learning management system (LMS) is a software application for the administration, documentation, tracking, reporting, automation, and delivery of educational courses, training programs, or learning and development programs. Developing rapport with instructors does not establish an LMS.
A syllabus is an academic document that communicates information about a specific course and defines expectations and responsibilities. While important, developing rapport with instructors does not establish a syllabus.
A support system refers to a network of people who provide an individual with practical or emotional support. Developing rapport with instructors can help online students feel more supported, receive guidance, and have a reliable resource for academic and personal challenges.
While developing a personal friendship with an instructor is possible, it is not the primary goal of establishing rapport in an academic setting. The main objective is to create a supportive and effective learning environment.