Ultrabornological space

In functional analysis, a topological vector space (TVS)

is called ultrabornological if every bounded linear operator from

A general version of the closed graph theorem holds for ultrabornological spaces.

is called bornivorous[2] if it absorbs every bounded subset of

is called infrabornivorous if it satisfies any of the following equivalent conditions: while if

locally convex and Hausdorff then we may add to this list:

Every Hausdorff sequentially complete bornological space is ultrabornological.

[citation needed] There exist ultrabarrelled spaces that are not ultrabornological.