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-

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

\dots m a t h e m a t i c a l a n a l y s i s \dots

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))