Loop space

In topology, a branch of mathematics, the loop space ΩX of a pointed topological space X is the space of based maps from the circle S to X with the compact-open topology. Two elements of a loop space can be naturally concatenated. With this concatenation operation, a loop space is an A_∞-space. The adjective A_∞ describes the manner in which concatenating loops is homotopy coherently associative.

单词	Loop space
释义	Loop space 英语百科 Loop space In topology, a branch of mathematics, the loop space ΩX of a pointed topological space X is the space of based maps from the circle S to X with the compact-open topology. Two elements of a loop space can be naturally concatenated. With this concatenation operation, a loop space is an A_∞-space. The adjective A_∞ describes the manner in which concatenating loops is homotopy coherently associative.
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