Talk:Bornological space

Etymology
Where does the name come from? --131.130.237.79 (talk) 12:36, 3 October 2013 (UTC)
 * The article now says where it comes from. — Preceding unsigned comment added by 2A00:23C4:7C87:4F00:D926:98E0:72B9:DBFB (talk) 08:57, 10 September 2020 (UTC)

Compact discs vs. complete discs
In the paragraph about Banach disks and ultrabornological spaces it is claimed that a ultrabornological X is equal to the inductive limit $$\operatorname{colim}\limits_{D\,\text{compact}} X_D$$. Is that really true? For bornological spaces the analogue colimit reduces to a single space where $D$ is choosen to be the unit sphere and in this sense the theorem bornological = colimit of normed reduced just to normed = normed. But for Banachspaces this cannot be true with the attribute "compact" lurking around. Any Banach space is ultrabornological, but one cannot simply choose the unit sphere here, because that is never compact in infinitedimensional spaces.

Should the criterion really use "compact" ? Isn't "complete" the right choice? — Preceding unsigned comment added by 92.231.92.81 (talk) 00:32, 14 April 2014 (UTC)

Bornological sets - a pedantic remark
The axioms of a bornological set as they are stated include the pair $$(\emptyset, \emptyset)$$. Is this intentional? For nonempty bornological sets it is clear, that the empty set is bounded. Wandynsky (talk) 23:28, 3 July 2019 (UTC)

Note
The second sentence in the first paragraph seems to be ungrammatical.