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complexnumber
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Homework Statement
Let [tex](X,d_X)[/tex] and [tex](Y,d_Y)[/tex] be metric spaces and let [tex]f: X \to Y[/tex].
Homework Equations
Prove that the following statements are equivalent:
1. [tex]f[/tex] is continuous on [tex]X[/tex],
2. [tex]\overline{f^{-1}(B)} \subseteq f^{-1}(\overline{B})[/tex] for all subsets [tex]B \subseteq Y[/tex]
The Attempt at a Solution
I an prove that (1) leads to (2) but don't know how to show (2) leads to (1). Can you give me some hint?