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for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.

1 vote

Continuity and sequential continuity of a linear functional

Another way of seeing that the answer is affirmative is to realize that the topology on $E$ is the inductive limit of the topologies on $C(K,R^m)$ (see e.g. https://en.wikipedia.org/wiki/Final_topolog …
Nicola Gigli's user avatar