Gamifying user experience while navigating knowledge structures is the new paradigm in online learning and improving human–computer interaction. Learning by playing and learning by doing lie at the core of this approach. Rooted in the paradigm of Conceptual Knowledge Processing and conceptual landscapes of knowledge, this research proposes an immersive experience in 3D knowledge structures, the VR FCA project. We exemplify this experience, at least the amount possible in a journal paper, by using data sets about topological spaces, a mathematical field which is notoriously hard to grasp by beginners or sometimes even at an intermediate level. We present the stages of this project, the technologies we have used in the implementation and also some basics of Formal Concept Analysis (FCA), the mathematical theory which lies at heart of Conceptual Knowledge Processing.

Given a normed space (X,||.||) and a linear (unbounded and not densely defined) operator A, defined on a subset D of X and with values in X, we show how to define norms |||.||| on X such that the operator A (viewed as an operator from D, endowed with the norm ||.||, with values in X, endowed with the norm |||.|||)) becomes bounded and D becomes dense with respect to |||.|||. We then apply our results to m-accretive operators.