Lifting Criterion

This lecture introduces the lifting criterion in the context of covering spaces and continuous maps. It explains the concept of a space having a certain property locally, such as being locally path connected. The lifting criterion states that a map from a path-connected and locally path-connected topological space can be lifted to a covering space if certain conditions on the fundamental groups are met. The proof involves constructing an explicit lift of the map and showing its continuity. The lecture emphasizes the importance of the space being locally path connected for the lifting process. By following a detailed step-by-step approach, the instructor demonstrates how to determine if a map can be lifted based on fundamental group properties.