English Dictionary

fundamental group

名詞

(topology) For a specified topological space, the group whose elements are homotopy classes of loops (images of some arbitrary closed interval whose endpoints are both mapped to a designated point) and whose group operation is concatenation.

日本語の意味

位相空間の各点における基準点を固定し、その点を通る閉路（ループ）のホモトピー同値類から得られる群。

The fundamental group of a topological space captures information about its loops up to homotopy and is a key invariant in algebraic topology.

位相空間の基本群は、そのループをホモトピー類として扱う群であり、代数的位相幾何学における重要な不変量です。

意味（1）

(topology) For a specified topological space, the group whose elements are homotopy classes of loops (images of some arbitrary closed interval whose endpoints are both mapped to a designated point) and whose group operation is concatenation.

From the definition it will be clear the group is a topological invariant of X; i.e., if two spaces are homeomorphic, their fundamental groups are isomorphic.

fundamental groups （ plural ）