April 15th, 2018, 12:06 PM  #1 
Newbie Joined: Jul 2014 From: Wrexham Posts: 20 Thanks: 0  Open covers
I’m using the usual Euclidean metric on ℝ^2 and the induced metric on P. Am I correct in thinking that a dpopen cover of P={(x, cosx) x∈ℝ} would be {(x, cosx) x∈(n,n):n∈ℕ}? Also is {ℝ^2} be a dopen cover that is finite and {(x,y)∈(n,n) y∈ℝ} be a dopen cover that is not finite? 
April 15th, 2018, 12:36 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,043 Thanks: 583 
What is a dp open cover? A d open cover? Please define any terms not in general use. The only meaning of dp I know is not suitable for a familyoriented website such as this. That's a set of isolated points in the plane. It's not an open set nor a collection of open sets. It couldn't be an open cover of anything. Last edited by Maschke; April 15th, 2018 at 12:38 PM. 
April 15th, 2018, 12:45 PM  #3 
Newbie Joined: Jul 2014 From: Wrexham Posts: 20 Thanks: 0  not that dp! The d part is emphasising that I'm using the Euclidean metric and the dp is emphasising I'm using the metric induced on P
Last edited by AJ235; April 15th, 2018 at 01:01 PM. 
April 15th, 2018, 01:25 PM  #4 
Newbie Joined: Jul 2014 From: Wrexham Posts: 20 Thanks: 0 
This is what I was given as an example. The blue is the dpopen cover.
Last edited by AJ235; April 15th, 2018 at 01:33 PM. 
April 17th, 2018, 07:57 AM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
As I said in your other post, under "Topology", a 'cover' has to be a collection of sets, not individual points so, no, this is not a cover for the set. I suspect that you intended to say {{(x, x^2)}: x∈n, n), n∈ N}, each member is the set of all such pairs, not individual pairs. Last edited by Country Boy; April 17th, 2018 at 08:11 AM. 

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covers, metric spaces, open, topology 
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