November 12th, 2016, 12:30 PM  #1 
Member Joined: Nov 2016 From: Kansas Posts: 56 Thanks: 0  Topological Space
Anyone?

November 12th, 2016, 02:01 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,344 Thanks: 534 
Let U be an open set in Y containing F(x). The inverse image of U is open in X and contains x. By assumption this set contains all but a finite number of x_n. Therefore U will contain the images F(x_n) (all but a finite number). This means that F(x_n) converges to F(x).


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space, topological 
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