1/ Let (X₁T) and (Y₁J.) be top spaces and fix-x be a surjective and continuousmap, then y is Compact Space when Xis Compact space)
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- Prove that topological space E is not homeomorphic to the spaceY = {(x, y) ∈ E^2 : y = ± x} (E represents R equipped with Euclidean distance, E^2 represents R^2 equipped with euclidean distance)Let f be a continuous mapping of a metric space X into metric space Y,g be a continuous mapping of metric space Y into metric space Z. Then gof ia a continues mapping of X into Zthe euclidean space R³ is a separable metric space. true or false?