...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


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Question Number 123794 by mnjuly1970 last updated on 28/Nov/20

$. . . m a t h e m a t i c a l a n a l y s i s . . .$ $s u p p o s e (X_{1}, τ_{1}) a n d (X_{2}, τ_{2})$ $a r e t w o t o p o l o g i c a l s p a c e s .$ $p r o v e f : (X_{1}, τ_{1}) \to (X_{2}, τ_{2}) i s$ $a c o n t i n u o u s f u n c t i o n i f o n l y$ $i f f o r a n y s u b s e t A \subseteq X_{1} :$ $f (c l (A)) \subseteq c l (f (A))$
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