Band (order theory)

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

Band (order theory)

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