It is currently Fri Aug 23, 2019 3:09 pm


All times are UTC [ DST ]




Post new topic Reply to topic  [ 1 post ] 
Author Message
 Post subject: Not closet set
PostPosted: Sat Mar 30, 2019 2:36 pm 
Team Member
User avatar

Joined: Mon Nov 09, 2015 1:36 am
Posts: 460
Location: Ioannina, Greece
Let $(X,\rho)$ a metric space and $(x_n)_{n\in{\mathbb{N}}}$ a Cauchy sequence in $X$, such that the set $\{x_n\;|\; n\in{\mathbb{N}}\}$ of the terms of this sequence it isn't a closed set. Prove that exists $x\in X$, such that $x_n\stackrel{\rho}{\longrightarrow}x$.

_________________
Grigorios Kostakos


Top
Offline Profile  
Reply with quote  

Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 1 post ] 

All times are UTC [ DST ]


Mathimatikoi Online

Users browsing this forum: No registered users and 0 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB® Forum Software © phpBB Group Color scheme created with Colorize It.
Theme created StylerBB.net