covering spaces
Covering spaces are a fundamental concept in algebraic topology that study the relationship between topological spaces and their continuous mappings to another space called the base space. A covering space is a topological space that maps onto the base space via a covering map, where each point in the base space has a neighborhood that is mapped homeomorphically to disjoint open sets in the covering space. Covering spaces provide a way to understand the fundamental group of a space by studying its associated covering spaces.
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