Can we expect that we might apply notions similar to "simple connectedness" and "multiple connectedness" to the $p$-adic setting, in spite of the fact that the standard topology of $\mathbb{Q}_p^n$ is totally disconnected. Hope this question make some sense.
Algebraic topology concepts in the $p$-adic setting
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p-adic-number-theory
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0@Zhen: Thank you for the advice. I will look into this. – 2011-10-25