November 12th, 2016, 12:30 PM  #1 
Member Joined: Nov 2016 From: Kansas Posts: 73 Thanks: 1  Topological Space
Anyone?

November 12th, 2016, 02:01 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,542 Thanks: 592 
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).


Tags 
space, topological 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Is there a topological space with fundamental group that does not contain anything?  Hayato  Topology  3  September 8th, 2015 03:52 PM 
Topological equivalence  Kzmo  Real Analysis  1  December 6th, 2013 09:54 AM 
topological question  golomorf  Real Analysis  4  February 1st, 2013 07:24 AM 
topological space involves open sets  fairyrak  Real Analysis  5  December 30th, 2011 05:39 PM 
Topological Space  Thomas Keyes  Real Analysis  1  November 24th, 2007 11:04 AM 