= Diagonal evaluation map
{title2=$\Delta(x)=(f_i(x))_{i\in I}$}
A family of maps with a common domain determines the displayed map into the <Cartesian product> of their codomains. It is injective exactly when the family separates points. For continuous coordinate maps it is continuous in the <product topology>. If inverse images of open sets under the coordinates generate the original topology, the inverse from the image is also continuous; thus the map is a <topological embedding>. A basis of such inverse images, as opposed to a subbasis, is a sufficient stronger hypothesis.
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