“product space”的概念、定义、翻译、参考文献-科学参考

product space

Mathematics

单词	product space
释义	product space Mathematics 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,d_X) and (Y,d_Y) are metric spaces, then $d ((x_{1}, y_{1}), (x_{2}, y_{2})) = d_{X} (x_{1}, x_{2}) + d_{Y} (y_{1}, y_{2})$ is a metric on X×Y which induces the product topology.
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