Recent content by seed21

Okay, here it is. I don't know if this is correct... Let A \in \tau such that f(x) \in A, then, f^-^1(A) \in \tau and x \in f^-^1(A) Since x_n \rightarrow x implies that \exists k \in \mathbb N such that x_n \in f^-^1(A) \forall n \succ k or given...

Hello. Please, help me with this exercise: Let X be a topological space and let Y be a metric space. Let f_n: X \rightarrow Y be a sequence of continuos functions. Let x_n be a sequence of points of X converging to x. Show that if the sequence (f_n) converges uniformly to f then...

That`s true. Thanks for help.

Homework Statement Let ( X, \tau_x) (Y, \tau_y) topological spaces, (x_n) an inheritance that converges at x \in X, and let f_*:X\rightarrow Y[/itex]. Then, [tex]f[/itex] is continuos, if given (x_n) that converges at [tex]x \in X , then [tex]f((x_n))[/itex] converges at...