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 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 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?
April 15th, 2018, 12:36 PM   #2
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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 family-oriented website such as this.

Quote:
 Originally Posted by AJ235 {(x, cosx) x∈(-n,n):n∈ℕ}?
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
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This is what I was given as an example. The blue is the dp-open cover.
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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: 3,264 Thanks: 902 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.

 Tags covers, metric spaces, open, topology

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