Topological Structure of Cadastral Space

Cadastral space may be the object of legal, geometric and topological analyses. Topological aspects, which are least recognized by the users, are deployed by IT specialists in the process of developing analytical applications. This study attempts to analyze the theoretical aspects of cadastral-topological space. Algebraic topology delivers a new approach by using a single mathematical formula to describe the structure of cadastral space. The algebraic notation is described by the block matrix T which characterizes the attributes of the analyzed matrix. The values of matrix T have been classified into three groups. Diagonal values describe the attributes of cadastral objects, the off-diagonal values of diagonal blocks indicate the connections between objects with the same geometry, whereas off-diagonal block matrices T describe the connections between objects with different geometry. Matrix T contains a full set of data which is normally presented in topological tables illustrating the correlations between boundary points, boundary lines and parcels. The value of matrix T was further modified by eliminating diagonal values that describe the attributes of cadastral objects and the attributes of their connections to produce matrix T Q , which describes only the topological relations between cadastral objects. The above relations were visualized with the use of graphs to demonstrate the practical applications of matrix T Q blocks.