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Homework Statement
Let f be a linear functional and set A=f-1({0})
Show that A is a closed linear subspace.
Homework Equations
The linearity comes from the fact that if f(a)=0 and f(b)=0 then f(βa+γb)=βf(a)+γf(b)=0
But how do we know it is closed? Do we show every sequence in A is convergent inside A or how do you show closedness for a space like this?