My Math Forum  

Go Back   My Math Forum > College Math Forum > Topology

Topology Topology Math Forum


Reply
 
LinkBack Thread Tools Display Modes
June 17th, 2010, 10:21 AM   #1
Newbie
 
Joined: Jun 2010

Posts: 2
Thanks: 0

discrete topology

SUPPOSE that has the discrete topology .prove that is separable if and only if is countable.
toti is offline  
 
June 17th, 2010, 02:58 PM   #2
Senior Member
 
Joined: Feb 2009

Posts: 172
Thanks: 5

Re: discrete topology

Consider with the discrete topology.

Suppose is separable. Then there exists wich is coutable and dense. Since is discrete for all . Hence, the only dense subset of is and so must be countable.

Suppose is coutable. Since is dense on itself we have that is separable.
parasio is offline  
Reply

  My Math Forum > College Math Forum > Topology

Tags
discrete, topology



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Help with Topology leonhardeuler Topology 8 February 26th, 2017 05:12 PM
Discrete sets and descrete topology bigli Topology 8 November 21st, 2013 11:54 AM
Problem on product topology/standard topology on R^2. vercammen Topology 1 October 19th, 2012 12:06 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





Copyright © 2019 My Math Forum. All rights reserved.