
Real Analysis Real Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 29th, 2014, 10:59 AM  #1 
Senior Member Joined: Sep 2010 From: Oslo, Norway Posts: 162 Thanks: 2  Showing that a space of functions is complete
Hello there, is the space of all bounded functions . I want to show that is complete. It is easy to show that indeed it is, and furthermore that all sequences of functions converge uniformly to elements in . But is this strictly necessary? Should it not be sufficient to show that pointwise? Is the uniform convergence critical to the completeness of X? And if yes, why? Thank you for your time. Kind regards, Marius Last edited by king.oslo; March 29th, 2014 at 11:09 AM. 
March 29th, 2014, 12:57 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,586 Thanks: 612 
In general, completeness in any metric space means convergence using the metric. The space of bounded functions uses a sup norm, so that means you need to show uniform convergence.


Tags 
complete, functions, showing, space 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Question on a vector space of functions  student42  Real Analysis  2  August 10th, 2013 05:59 AM 
Space trapped between functions  OriaG  Calculus  3  August 29th, 2012 11:56 AM 
space of psummable sequences complete?  e161065  Real Analysis  3  April 25th, 2010 03:49 AM 
Space of bounded functions  saxash  Abstract Algebra  0  November 24th, 2009 03:02 AM 
Vector functions & space curves  remeday86  Calculus  1  February 16th, 2009 04:43 PM 