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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?