Abstract
Every locally convex space is a topological group, that is, a group that is also a topological space in which the group operations (multiplication and inversion) are continuous. A large number of the most basic results about locally convex spaces are actually valid for any topological group and can be established in that context with only a little additional effort. Since topological groups are important in their own right, it seems worthwhile to establish these basic results in the context of topological groups.
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Osborne, M.S. (2014). Topological Groups. In: Locally Convex Spaces. Graduate Texts in Mathematics, vol 269. Springer, Cham. https://doi.org/10.1007/978-3-319-02045-7_1
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DOI: https://doi.org/10.1007/978-3-319-02045-7_1
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