
Topology Topology Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 16th, 2012, 02:55 AM  #1 
Newbie Joined: Oct 2012 Posts: 4 Thanks: 0  Problem on product topology/standard topology on R^2.
Let $\mathbb{R}_{\tau}$ be the set of real numbers with topology $\tau = \{(x,x) x>0\} \cup \{\emptyset, \mathbb{R}\}$ and $\mathbb{R}_{\tau} \times \mathbb{R}_{\tau}$ be the product topology on $\mathbb{R}^2$. a)Prove that $A = \{(x,y) \in \mathbb{R}^2  x^2 + y^2 < 1\}$ is open in $\mathbb{R}_{\tau} \times \mathbb{R}_{\tau}$ b)Find $\overline{A}$.Justify your answer. c) What functions $f: {\mathbb{R}_{\tau}}^2 \rightarrow \mathbb{R}$ are continuous? Here $\mathbb{R}$ has the standard topology and ${\mathbb{R}_{\tau}}^2 = \mathbb{R}_{\tau} \times \mathbb{R}_{\tau}$ has the product topology. PICTURE ATTACHED! Please help! 
October 19th, 2012, 12:06 PM  #2 
Member Joined: Jul 2011 From: Trieste but ever Naples in my heart! Italy, UE. Posts: 62 Thanks: 0 
You start to draw (U.F.O. topology or shooting topology) on so you'll ask to question a and b.


Tags 
problem, product, topology, topology or standard 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Continuity of fog and f/g on standard topology.  vercammen  Topology  2  October 19th, 2012 01:04 PM 
Homeomorphism in R^2. Standard Topology.  vercammen  Topology  1  October 19th, 2012 11:47 AM 
Product Topology  matthematical  Topology  2  September 20th, 2011 03:20 PM 
discrete topology, product topology  genoatopologist  Topology  0  December 6th, 2008 11:09 AM 
discrete topology, product topology  Erdos32212  Topology  0  December 2nd, 2008 02:04 PM 