Path space (algebraic topology)

In algebraic topology, a branch of mathematics, the based path space

is the space that consists of all maps

, called based paths.

[1] In other words, it is the mapping space from

to X, with no distinguished point for the start of the paths, is called the free path space of X.

to X are called free paths.

[1] The natural map

is a fibration called the path space fibration.

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