Let \(M \in \mathcal{M}_{T, \text { loc }}^{c}\). Show that the following maps are continuous, if we use ucpconvergence in both range and domain:

a) \(\mathcal{L}_{T, \text { loc }}^{2}(M) i f \mapsto f^{2} \cdot\langle Mangle\).

b) \(\mathcal{L}_{T, \text { loc }}^{2}(M) i f \mapsto f \bullet M \in \mathcal{M}_{T, \text { loc }}^{c}\).

c) \(\mathcal{M}_{T, \text { loc }}^{c} i M \mapsto\langle Mangle\).