
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 2nd, 2015, 06:23 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 470 Thanks: 1  An example of a compact multiplicatively unbounded ring
My teacher asked me to build an associative topological Hausdorff compact ring $\displaystyle R$ with 1, which is multiplicatively unbounded. That means there is a neighborhood $\displaystyle U∋1$ such that $\displaystyle FU≠R$ for each finite subset $\displaystyle F$ of $\displaystyle R$. I am somewhat stuck, because I have a small stock of topological rings, and I see only two main ways to build such an example: to endow a compact topological group with a multiplication or to endow a ring with a compact ring topology. Both of these ways require a concordance of many conditions and therefore it seems to me that my success of the construction “depends on luck, but not on method”. 

Tags 
compact, multiplicatively, ring, unbounded 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
measure of unbounded set  James1973  Advanced Statistics  2  October 14th, 2013 02:34 AM 
Unbounded function on a closed graph  abcdefgh  Real Analysis  3  May 31st, 2012 02:23 AM 
Range of a compact set is compact  keremaytac  Real Analysis  7  January 7th, 2012 08:14 AM 
Complex Unbounded Sets  BelaTalbot  Complex Analysis  1  March 5th, 2010 04:57 AM 
unbounded sequence  rose3  Real Analysis  4  December 9th, 2009 01:20 PM 