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mathematical-analysis-suppose-X-1-1-and-X-2-2-are-two-topological-spaces-prove-f-X-1-1-X-2-2-is-a-continuous-function-if-only-if-for-any-subset-A-X-1-

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Question Number 123794 by mnjuly1970 last updated on 28/Nov/20
...mathematical analysis... suppose (X_1 ,τ_1 ) and (X_2 ,τ_2 ) are two topological spaces. prove f:(X_1 ,τ_1 )→(X_2 ,τ_2 ) is a continuous function if only if for any subset A⊆X_1 : f(cl(A))⊆cl(f(A))
…mathematicalanalysis…suppose(X1,τ1)and(X2,τ2)aretwotopologicalspaces.provef:(X1,τ1)→(X2,τ2)isacontinuousfunctionifonlyifforanysubsetA⊆X1:f(cl(A))⊆cl(f(A))

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