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math.FA2026
A homological approach to (Grothendieck's) completeness problem for regular LB-spaces
Sven-Ake Wegner
We consider the long-standing question of whether every regular LB-space is complete. This problem has been open since the 1950s and originates in Grothendieck's early work in func…
math.FA2025
Condensed mathematics through compactological spaces
Franziska Böhnlein, Benjamin Bruske, Sven-Ake Wegner
In their 2022 lecture notes on condensed sets, Clausen and Scholze mentioned in a remark that the important subclass of quasiseparated condensed sets is equivalent to the category…
math.FA2025
Bornological LB-spaces and idempotent adjunctions
Jack Kelly, Lenny Neyt, Sven-Ake Wegner
The notion of an LB-space was introduced by Grothendieck in his 1953 thèse, referring to a countable colimit of Banach spaces taken within the category of locally convex topologic…