5 papers
Homological surrogates in topological and bornological analysis
Marianne M. Lawson, Sven A. Wegner
We describe hearts of strongly deflation-exact categories with kernels as localizations of categories of three-term complexes up to homotopy, without assuming admissibility of kern…
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…
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…
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 topologica…
An in-depth look at approximation via deep and narrow neural networks
Joris Dommel, Sven A. Wegner
In 2017, Hanin and Sellke showed that the class of arbitrarily deep, real-valued, feed-forward and ReLU-activated networks of width w forms a dense subset of the space of continuou…