On Intermediate Factors of a Product of Disjoint Systems

Key Points

• The central aim is to explore intermediate factor situations in ergodic theory and topological dynamics.
• Proving a master-key theorem in probability measure preserving ergodic theory.
• Examining numerous applications of the master-key theorem.
• Analyzing a case of topological dynamics with a distal system.
• Providing counterexamples related to the studied systems.
• The master-key theorem offers a foundational understanding in ergodic theory.
• A diverse range of applications demonstrates the theorem's relevance.
• Counterexamples highlight limitations in certain topological dynamic scenarios.