(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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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# Homework Help: Counterexample Topology

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