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Convergence of series, sequences and functions and different modes of convergence.

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How general is the convergence of the exponential function's power series?

Suppose that $N$ is the set of all continuous semi-norms in $V$. For every semi-norm $p\in N$ there exists semi-norm $q \in N$ such that $p(\beta(a,b)) \leq q(a)q(b)$ --- this is a consequence of the …
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