A simplicial complex is a mathematical structure that consists of a set of vertices, edges, triangles, and higher-dimensional analogs, organized in a way that captures the topological features of a space. Each element of a simplicial complex is called a simplex, and the collection of these simplices satisfies certain intersection properties that allow for the construction of more complex shapes. This concept is crucial in understanding the foundational aspects of algebraic topology, particularly in the study of singular homology and cohomology.
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