The authors consider \({\mathcal{C}}^1\)-functionals \(G:E\to\mathbb R\) defined on a separable Hilbert space \(E\) so that \(G':E\to E\) is weakly sequentially continuous. By definition, a subset \(A\) of \(E\) links \(D\subset E\) weakly if each such \(G\) satisfying \(\text{{sup}}\, G(A)\leq\text{{inf}}\,G(B)\) has a \((PS)_c\)-sequence for some \(c\geq\text{{inf}}\,G(B)\). For instance, if \(E=M\oplus N\) is the direct sum of closed linear subspaces then \(A=\partial B_r\cap N\) links \(B=M\) weakly; here \(\partial B_r\) denotes the boundary of the closed ball of radius \(r>0\) in \(E\). \(M\) and \(N\) may both be infinite-dimensional. The same is true for \(A=(B_R\cap N)\cup\{s w_0+v: v\in N\), \(s\geq 0\), \(\| s w_0+v\| =R\}\) and \(B=\partial B_r\cap M\), some \(w_0\in M\setminus\{0\}\), \(0