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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. [1] 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. [2] The path space can then be viewed as the pullback of along . [1]

The natural map is a fibration called the path space fibration. [3]


  1. ^ a b Martin Frankland, Math 527 - Homotopy Theory - Fiber sequences
  2. ^ Davis & Kirk 2001, Definition 6.14.
  3. ^ Davis & Kirk 2001, Theorem 6.15. 2.
  • Davis, James F.; Kirk, Paul (2001). Lecture Notes in Algebraic Topology (PDF). Graduate Studies in Mathematics. Vol. 35. Providence, RI: American Mathematical Society. pp. xvi+367. doi: 10.1090/gsm/035. ISBN  0-8218-2160-1. MR  1841974.

Further reading