Nonarchimedean Functional Analysis by Peter Schneider (Hardback, 2001)

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The course covered the material which here is presented in the first three chapters. In its deeper aspects the theory depends very much on the field being spherically complete or not. To give a drastic example, if the field is not spherically complete then there exist nonzero locally convex vector spaces which do not have a single nonzero continuous linear form.
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