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Homework Statement
Let [tex]( X, \tau_x)[/tex] [tex] (Y, \tau_y)[/tex] topological spaces, [itex](x_n)[/itex] an inheritance that converges at [tex]x \in X[/tex], and let [tex]f_*:X\rightarrow Y[/itex].
Then, [tex]f[/itex] is continuos, if given [itex](x_n)[/itex] that converges at [tex]x \in X [/tex], then [tex]f((x_n))[/itex] converges at [tex]f(x)[/itex].
I need a counter example, to prove that the reciprocal is not true.
All I know is that X should not be first countable.
Please, help me.
Thanks in advance.
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