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In order to study the topological properties of complex shapes, it is convenient to view them as the union of simplex gluing together in a specific manner to form simplicial complexes. Simplex are the simple geometric objects like points, line segments, triangles, tetrahedra etc. Layer Topology on simplicial complexes helps us to understand the topological properties of complex shapes by comparing the topological properties of closed unit interval in the usual topology.

Layer topology on vertex chain simplicial complexes