English Dictionary

product topology

名詞

(topology) The topology of the Cartesian product of two or more topological spaces which is generated from a basis whose elements are Cartesian products of open subsets of the original spaces, such that for each such Cartesian product only a finite quantity of such subsets are proper.

日本語の意味

積位相（もしくは直積位相）: 複数の位相空間の直積集合上に定められる位相。各元において、有限個の要素でのみ元となる空間の開集合が厳選され、他は全体集合となる開集合の直積を基本系として生成される位相。

When considering infinite products of topological spaces, the product topology is defined so that a set is open if it is a union of basic open sets in which only finitely many coordinates are proper open subsets of the corresponding spaces.

位相空間の無限直積を考えるとき、直積位相は、ある集合が開であるためには、それが対応する空間のうち有限個のみが真の開集合となるような基本開集合の合併として表せるように定義される。

意味（1）

(topology) The topology of the Cartesian product of two or more topological spaces which is generated from a basis whose elements are Cartesian products of open subsets of the original spaces, such that for each such Cartesian product only a finite quantity of such subsets are proper.

product topologies （ plural ）