{\displaystyle X} is bornivorous if it is bornivorous with respect to the von-Neumann bornology of X {\displaystyle X} . Bornivorous sets play an important...

{\displaystyle A} is bornivorous if it absorbs every bounded balanced set and in a convex vector bornology A {\displaystyle A} is bornivorous if it absorbs every...

and balanced set Balanced set – Construct in functional analysis Bornivorous set – A set that can absorb any bounded subset Bounded set (topological vector...

{\displaystyle X} is called bornivorous and a bornivore if it absorbs every bounded subset of X . {\displaystyle X.} Every bornivorous subset of X {\displaystyle...

operators are continuous Bornivorous set – A set that can absorb any bounded subset Bounded function – A mathematical function the set of whose values is bounded...

{\displaystyle X} such that S V ⊆ U . {\displaystyle SV\subseteq U.} Bornivorous set – A set that can absorb any bounded subset Bornological space – Space where...

vector bornology on C ( T , K ) . {\displaystyle C(T,\mathbb {K} ).} Bornivorous set Bornological space Bornology Space of linear maps Ultrabornological...

relatively compact set is totally bounded and the closure of a totally bounded set is totally bounded. The image of a totally bounded set under a uniformly...

barrel (resp. bornivorous barrel, bornivorous disk) in M {\displaystyle M} then there exists a barrel (resp. bornivorous barrel, bornivorous disk) C {\displaystyle...

quasibarrelled spaces are topological vector spaces (TVS) for which every bornivorous barrelled set in the space is a neighbourhood of the origin. Quasibarrelled...

bounded disks. F − 1 {\displaystyle F^{-1}} maps bornivorous disks in Y {\displaystyle Y} into bornivorous disks in X . {\displaystyle X.} if X {\displaystyle...

space (TVS). A disk is a convex and balanced set. A disk in a TVS X {\displaystyle X} is called bornivorous if it absorbs every bounded subset of X . {\displaystyle...