Raising, analyzing and solving problems are the core competitiveness factors of innovative talent. However, to date the mechanism for problem cognition has not been elucidated and still needs to be studied. A problem space is the representation of the sum of cognitive conditions, cognitive objectives, cognitive rules, cognitive impairment, and cognitive situation, and is a high-dimensional manifold. The observation and dimensionality reduction of problem spaces are considered as problem areas. Human-computer coupled cognitive observation is a new method for studying the brain at the information level, and can also be used in the observation of problem spaces. In this paper the human-computer coupled cognitive environment is established and a problem situation is constructed. Additionally problem objects are marked, data for raising problems are collected to establish a set of problem objects, and a tree topology is selected as the structure of the low-dimensional problem space to reconstruct a problem space. It is felt that the observation, dimensionality reduction, visualization, and topologization of problem spaces provide foundations for evidence-based and dynamic studies on problem spaces, as well as providing support for teaching.