English Dictionary

homotopy

名詞

可算名詞 不可算名詞 略語 別表記 省略 くだけた表現

(topology) A continuous deformation of one continuous function or map to another. / (uncountable) The relationship between two continuous functions where homotopy from one to the other is evident.

日本語の意味

位相幾何学において、ある連続写像が別の連続写像へ連続的に変形できること。 / 二つの連続写像が、互いに連続変形可能であるという関係性。

In algebraic topology, we studied a homotopy between two continuous maps and computed the induced map on fundamental groups.

代数位相学では、2つの連続写像の間の連続変形（ホモトピー）を調べ、それが基本群に与える誘導写像を計算しました。

意味（1）

(topology) A continuous deformation of one continuous function or map to another.

The concept of homotopy represents a formalisation of the intuitive idea of a smooth deformation of one curve into another.

意味（2）

(uncountable) The relationship between two continuous functions where homotopy from one to the other is evident.

意味（3）

(informal) Ellipsis of homotopy theory. (the systematic study of homotopies and their equivalence classes).

意味（4）

(topology) A theory associating a system of groups with each topological space.

意味（5）

(topology) A system of groups associated with a topological space.

homotopies （ plural ）