Do you really want to send mummert a message saying you like their work?
A kind of a normed space or a vector space with a particular inner product function from the vector space crossed with itself into the metric space of that vector space. If you understood the preceding sentence, then you are a mathematician. Note: the square root of the inner product function gives rise to the norm of the normed space.
although there are some normed spaces for which there is no corresponding inner product. viz l-infinity norm
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