My Math Forum Problem on product topology/standard topology on R^2.

 Topology Topology Math Forum

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!

Attached Images
 5.png (99.1 KB, 227 views)

 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 $\tau$ (U.F.O. topology or shooting topology) on $\mathbb{R}$ so you'll ask to question a and b.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post vercammen Topology 2 October 19th, 2012 01:04 PM vercammen Topology 1 October 19th, 2012 11:47 AM matthematical Topology 2 September 20th, 2011 03:20 PM genoatopologist Topology 0 December 6th, 2008 11:09 AM Erdos32212 Topology 0 December 2nd, 2008 02:04 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top