My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 10th, 2014, 09:53 AM   #1
Member
 
matthematical's Avatar
 
Joined: Jun 2011
From: California

Posts: 82
Thanks: 3

Math Focus: Topology
Equivalence Relation Question

Hi all!

I'm reading right now about the quotient topology and quotient spaces, and I've come across an example that uses this statement:

"On $\mathbb{R}^2$, let $\equiv$ be the equivalence relation generated by $(x, y) \equiv (-x, y)$."

I'm not familiar with this treatment of equivalence relations; I'm used to a book explicitly defining an equivalence relation in the way of "$(x, y) \equiv (a, b)$ if and only if . . ." .

Do I just treat this as "The equivalence relation on $\mathbb{R}^2$ such that every point $(x, y)$ is related to the point $(x, y)$"?

If not, how do treat this? Having a Master's, I'm well acquainted with equivalence relations, but I'm hoping I wasn't just spacing out as an undergrad on the day equivalence relations were taught in my introductory proofs class.

Last edited by matthematical; October 10th, 2014 at 09:57 AM.
matthematical is offline  
 
October 10th, 2014, 02:46 PM   #2
Senior Member
 
Joined: Dec 2013
From: Russia

Posts: 327
Thanks: 108

Quote:
Originally Posted by matthematical View Post
"On $\mathbb{R}^2$, let $\equiv$ be the equivalence relation generated by $(x, y) \equiv (-x, y)$."
This means that $\equiv$ is the reflexive, symmetric and transitive closure of the given relation, i.e., the smallest equivalence relation containing the given one. In this case, one only has to take the reflexive closure, I believe.
Evgeny.Makarov is offline  
Reply

  My Math Forum > College Math Forum > Abstract Algebra

Tags
equivalence, question, relation



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Equivalence relation tom33 Algebra 3 January 17th, 2014 04:30 PM
Equivalence Relation Taladhis Abstract Algebra 2 February 11th, 2013 08:20 AM
Equivalence Relation jrklx250s Real Analysis 3 December 7th, 2011 10:42 AM
Equivalence Relation question jstarks4444 Number Theory 1 October 30th, 2011 06:39 PM
equivalence relation tinynerdi Abstract Algebra 1 January 11th, 2010 09:24 AM





Copyright © 2018 My Math Forum. All rights reserved.