The article proposes a new approach to the competencies assessment based on the knowledge space model represented as an algebraic structure (lattice). In contrast to the existing approach, suggested by Doignon and Falmagne within their Knowledge Space Theory (KST), using lattice makes it possible to build knowledge space without constructing large combinatorial structures. Each competence is matched to a subspace of the knowledge space, the study of which means mastering corresponding competence. The set of intersecting subspaces determines the topology of competences on the knowledge space. The level of each competence is evaluated by a pair of differential and integral assessments. The results of the competencies assessment are visualized in the form of heat maps. The proposed approach allows both to evaluate individual competencies mastering and to compare the results of competencies assessments obtained by different students.