The purpose of this paper is to pose a new question to speed-up mutual understanding among team members or/and group of experts when communicating over the Internet in forms of virtual collaboration, electronic brainstorming, network strategic conversation, etc. We have previously proposed an approach that the convergent control mechanism based on the fundamental principles of thermodynamic and inverse problem solution method, as well as various artificial intelligence techniques, be incorporated into the communicative process. This paper shows a further development of the approach in terms of applying The Fuzzy Tychonoff Theorem along with quantum techniques provide to reach a high level of holistic discourse which is achieved not only through the application of fundamental principles of compactness of the topological space, but also utilizing quantum entanglement and complementarity principles for discourse structuring in a special way. The approach is implemented as the Responsibility Thinking System (RTS) tested in the course of finding the decisions of the real life issues.