Open mapping theorem, Let P : C -> R be defined by P(z) =

Open mapping theorem

Reference no: EM13127624

Let P : C -> R be defined by P(z) = Re z; show that P is an open map but it is not a closed map. ( Hint: Consider the set F = { z : Imz = ( Re z)^-1 and Re z doesn't equal to 0}.) Please explain every step and justify.

Reference no: EM13127624

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