The term 'closed' and also the term 'complete' are used to describe
vectors and spaces in quantum mechanics.
A set of vectors is 'closed' if a sequence of vectors converges to a
vector which is also a member of the set.
A space is complete if every Cauchy sequence of vectors converges to a
limit vector that is also in the space.
These two terms seem to say the same thing - it's pretty difficult for
me to be able to understand why they don't amount to the same thing -
they both refer to converging vectors.
Perhaps one way might be if someone could give an example of a set of
closed vectors that does not live in a complete space.
Or/Also a complete space that admits a set of vectors that isn't closed.
Thanks for any help.
David.


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