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I want some notes about $p$-adic Topology and some properties with proves about $\mathbb{Z}$ with this Topology.

Thank you.

share|cite|improve this question for example – Beni Bogosel Oct 6 '12 at 16:44
Thanks my friend – Wreza Shafaghi Oct 7 '12 at 20:44

This will actually cost you some money (though it is relatively cheap), not sure if you're against that, but I loved the book "p-adic Analysis Compared with Real" by Svetlana Katok. It does a great job of helping you understand exactly where $p$-adic numbers come from and how to calculate with them. If you understand real analysis, you will understand this stuff. It's written at an advanced undergraduate level. As an okay grad student at an okay school, I find it very easy to learn from.

And, specifically, Chapter 2 is "The Topology of $\mathbb{Q}_p$ vs. The Topology of $\mathbb{R}$".

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