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In regards to a Metric space

A metric space is an ordered pair (M,d) where M is a set and d is a metric on M, i.e., a function

[itex]{{\bf{d: M \times M}}}[/itex] (the syntax here)

such that for any x,y,z [itex] \in \bf{M}[/itex] (and the e looking symbol)

Does the times symbol in the first part indicate an M by M matrix, how would this be read. And the e symbol which I don't know the name of, I believe is akin to saying all numbers in, or every set in the space, or something roughly like that. So, how would I read the whole thing given the mathematical statement as written above if there was no explanation surrounding it? I have a lot of trouble reading pure math books sometimes because I don't understand a lot of the simple notation, even though I've seen the material before. I don't necessarily know how to represent the statement mathematically, for instance if I wanted to say something like a function that takes all real numbers as arguments, or considering all real numbers.