User blog comment:Alemagno12/Question/@comment-35470197-20180730015542/@comment-35470197-20180801065039

Not exactly. Even if the condition \(\textrm{cof}(x) = \textrm{cof}(b)\), is simply replaced by \(\textrm{cof}(a) = \textrm{cof}(b)\), then \(H_{\omega}(\Omega,\Omega)\) will not be well-defined.