My Math Forum  

Go Back   My Math Forum > College Math Forum > Topology

Topology Topology Math Forum


Thanks Tree1Thanks
  • 1 Post By Country Boy
Reply
 
LinkBack Thread Tools Display Modes
April 15th, 2018, 12:12 PM   #1
Newbie
 
Joined: Jul 2014
From: Wrexham

Posts: 20
Thanks: 0

Open cover

I’m using the usual Euclidean metric on ℝ^2 and the induced metric on P.

Am I correct in thinking that a dp-open cover of

P={(x, cosx) x∈ℝ}

would be

{(x, cosx) x∈(-n,n):n∈ℕ}?

Also is {ℝ^2} be a d-open cover that is finite and {(x,y)∈(-n,n) y∈ℝ} be a d-open cover that is not finite?
AJ235 is offline  
 
April 17th, 2018, 07:51 AM   #2
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,198
Thanks: 872

Quote:
Originally Posted by AJ235 View Post
I’m using the usual Euclidean metric on ℝ^2 and the induced metric on P.

Am I correct in thinking that a dp-open cover of

P={(x, cosx) x∈ℝ}

would be

{(x, cosx) x∈(-n,n):n∈ℕ}?
The way you have written this, no, it is not a cover, it is a collection of individual points, not open sets. It does include all real numbers but not sets of real numbers.

Quote:
Also is {ℝ^2} be a d-open cover that is finite and {(x,y)∈(-n,n) y∈ℝ} be a d-open cover that is not finite?
Yes, R^2 is the set of all pairs of real numbers so that single set covers all of R^2 and so any subset of it. The other, {(x,y)∈(-n,n) y∈ℝ}, is again a collection of individual points, not a collection of sets.
Thanks from cjem
Country Boy is online now  
Reply

  My Math Forum > College Math Forum > Topology

Tags
cover, open



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
How many mathematics textbooks is it realistic to study cover to cover mathsman1 Math 3 November 30th, 2015 11:37 AM
Topics To cover Calc 2 Dan3500 Calculus 3 July 3rd, 2013 09:36 PM
Open Cover/Subcover Problem Hammerton Real Analysis 3 January 17th, 2013 05:29 PM
Find an open cover without a finite subcover Singularity Real Analysis 1 February 15th, 2012 01:21 PM
I was looking at some old math book cover and realise that MyNameIsVu Linear Algebra 1 July 14th, 2009 07:01 PM





Copyright © 2018 My Math Forum. All rights reserved.