What is the projection of the empty set?

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axeae
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I'm wondering if the projection of the empty set has been defined? several books I've read seem to regard it in different ways
 

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I wasn't aware that the projection of a set had been defined in general! I know about the projection of some subset of a linear space on a subspace- is that what you are thinking about? In that case the projection of the empty set onto any subspace is the empty set.

Perhaps it would help if you showed some of the "different ways" in which it is regarded.
 
that's what I was thinking of, I had assumed it was that but the books kind of avoided addressing it directly
 

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