Topological models of propositional logic of problems and propositions

The propositional fragment $\mathrm{HC}$ of the joint logic of problems and propositions introduced by S. A. Melikhov is considered. Topological models of this logic are constructed and the completeness of the logic $\mathrm{HC}$ with respect to this type of models is shown. Topological models of the logic $\mathrm{H}4$ introduced by S. Artemov and T. Protopopescu are also constructed.