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.