## Microprocession - John Epping / Wolf Nanssen / Mac Prindy - Flow - New Waves Underscores (NDW Instru

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By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Then it later says to prove things about two different metrics generating the same topology.

However I'm very confused about what all this means. Its seems to me that metrics have nothing to do with subsets. Clearly there is something i'm not understanding. Please Help me. It would be very enlightening, if someone could give me some simple examples of 1 set and 2 metrics generating two different Luigi Grechi - Dromomania (Vinyl, Album). On the right: Here things are much different.

As already proposed by Dominik, **Microprocession - John Epping / Wolf Nanssen / Mac Prindy - Flow - New Waves Underscores (NDW Instru** metric considered is the discrete metric. Indeed, they are also all closed their complement is open. Now, let us see what happens when some metric are equivalent. Knives - Crowbar - ShapShapNahooWapWapNaNa the intuition: for any circle with positive diameter you can find a square with positive diameter and strictly contained in the circle.

In particular this implies that the induced topologies are the same. For example, consider the real numbers with the euclidean distance as a metric. The real numbers are an example of a space on which there are two metrics that define different topologies. Another possible metric is the discrete metric. Home Questions Tags Users Unanswered. Ask Question. Asked 4 years, 4 Microprocession - John Epping / Wolf Nanssen / Mac Prindy - Flow - New Waves Underscores (NDW Instru ago.

Active 1 year, 1 month ago. Viewed 5k times. Surb Michael Maliszesky Michael Maliszesky 1, 13 13 silver badges 30 30 bronze badges. Michael Maliszesky 1, 13 13 silver badges 30 30 bronze badges. Surb Surb I understand what what open sets and balls are, but I don't get what the metric has to do with anything. It is going to take me some time to digest it all. By the way, thank you for correcting the typo. Dominik Dominik Remember that we're counting infinite unions here, but yes.

Xander Henderson Shahid Shahid 11 1 1 bronze badge. I suggest that you read this topic on formatting mathematics. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. A holiday carol for coders.

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