 If "L" is another open and closed set in the subspace topology on "σ"("T") then "P"("K";"T")"P"("L";"T") = "P"("L";"T")"P"("K";"T") = "P"("K" ∩ "L";"T") which is zero whenever "K" and "L" are disjoint.Spectral projections have numerous applications.Any isolated point of σ("T") is both open and closed in the subspace topology and therefore has an associated spectral projection.