- . Let Zn, z be points in C and let d be the chordal metric on Co. Show that zn z → 0 if and only if d(zn, 2)→0. Also show that if |zn| →∞ then {n} is Cauchy in Co. (Must {n} converge in C?)

Let f ∈ L (U, V ), g ∈ L (V, W) and let U, V be finite-dimensional. Prove that(a) dim im(g ◦ f) = dim im f − dim(ker g ∩ im f) and so dim im(g ◦ f) ≤ min(dim im f, dim im g);(b) dim ker(g ◦ f) = dim ker f + dim(ker g ∩ im f) and so dim ker(g ◦ f) ≤ dim ker f + dim ker g.

let f:X→R Cont & X is bounded&clused then f is unifurmly cont.

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