“product space”的概念、定义、习题解题方法及翻译-数学辞典

单词

product space

释义

product space

Given topological spaces X and Y, the product space topology on the Cartesian product X×Y has the sets U×V, where U is open in X and V is open in Y, as a basis. The product topology on R×R is the same as the topology on R2, though the basic open sets for the former might be considered as open rectangles and for the latter open discs.

If (X,dX) and (Y,dY) are metric spaces, then

is a metric on X×Y which induces the product topology.

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