English Dictionary

loopspace

名詞

(mathematics) A function space of continuous functions that map from the unit interval to a space from x₀ to x₁, all of which map 0 to x₀ and 1 to x₁.

日本語の意味

（数学）単位区間 [0,1] から始点 x₀ と終点 x₁ を持つ空間への連続写像全体からなる関数空間。各写像は 0 を x₀ に、1 を x₁ に写す。

In homotopy theory, the loopspace of a topological space relative to points x₀ and x₁ is the set of all continuous functions from the unit interval to that space which send 0 to x₀ and 1 to x₁.

ホモトピー論において、x₀からx₁への経路の空間は、単位区間からその空間への連続写像で、0をx₀に、1をx₁に送るもの全体から構成される。

意味（1）

(mathematics) A function space of continuous functions that map from the unit interval to a space from x₀ to x₁, all of which map 0 to x₀ and 1 to x₁.

Ravenel's: Infinite loopspace theorists, where are you?, or more prosaically: Can one start from the notion of Ring Spectrum Representing Formal Group Laws (the functor) and arrive at Complex Cobordism? Our answer is a tentative sort-of..

loopspaces （ plural ）