Homeomorphic Equivalences of Huye Museum Shapes as Topological Spaces: Analyzing Cultural Heritage Structures Through Topological Methods

In this work, we study the properties of Huye Museum Shapes that we regard as topological subspaces of the Euclidean plane ℝ². The properties under consideration are number of connected components and number of holes. We further look at the classification of these spaces by using the concepts of homeomorphism. Among the 50 considered spaces, we show that there are only 36 spaces that are not homeomorphic, this means that there are 36 equivalence classes with respect to homeomorphism equivalence. Each of those 50 spaces might be classified in one of those 36 distinct equivalence class.