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In algebraic topology, a branch of mathematics, the path space of a based space is the space that consists of all maps from the interval to X such that , called paths. In other words, it is the mapping space from to . The space of all maps from to X (free paths or just paths) is called the free path space of X. The path space can then be viewed as the pullback of along . The natural map is a fibration called the path space fibration.
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