LB-ness of completions of LB-spaces

Determine whether the (usual) completion \widehat{X} of any LB-space X is again an LB-space.

Background

The categorical and homological framework in the paper relies on working within LB-spaces. If completions of LB-spaces were always LB-spaces, several constructions would be simpler and relate directly to classical completeness questions. The authors highlight that even this structural property is presently unknown.

References

  1. It is unknown if the completion $\widehat{X}$ of an LB-space $X$ is always an LB-space.
— A homological approach to (Grothendieck's) completeness problem for regular LB-spaces  (2512.13161 - Wegner, 15 Dec 2025) in Section “Complete LB-spaces” (SEC-COM), opening paragraph