Definition. Let $X$ be a Banach space. A mapping $f:[a,b]\to X$ is called regulated if it has one sided limits.
In the setting of a Hausdorff topological vector space $X$, can we still define regulated functions?
2026-03-31 12:10:15.1774959015
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As in a Hausdorff topological vector space the one sided limit of a function is a defined object, you surely can do this, exactly as in the case of Banach spaces. (You even do not need the Hausdorff condition or vector space structure, as "having a limit" does not need this).