1 Answers
In mathematics, specifically in order theory and functional analysis, a band in a vector lattice X {\displaystyle X} is a subspace M {\displaystyle M} of X {\displaystyle X} that is solid and such that for all S ⊆ M {\displaystyle S\subseteq M} such that x = sup S {\displaystyle x=\sup S} exists in X , {\displaystyle X,} we have x ∈ M . {\displaystyle x\in M.} The smallest band containing a subset S {\displaystyle S} of X {\displaystyle X} is called the band generated by S {\displaystyle S} in X . {\displaystyle X.} A band generated by a singleton set is called a principal band.