In combinatorics, an abstract simplicial complex (ASC), often called an abstract complex or just a complex, is a family of sets that is closed under taking...

counterpart to a simplicial complex is an abstract simplicial complex. To distinguish a simplicial complex from an abstract simplicial complex, the former...

information about the local structure of the complex at the vertex. Given an abstract simplicial complex X and v {\textstyle v} a vertex in V ( X ) {\textstyle...

: sec.5.3.2  Simplicial homology is defined by a simple recipe for any abstract simplicial complex. It is a remarkable fact that simplicial homology only...

is topological properties of simplicial complexes and its generalization, cell-complexes. An abstract simplicial complex above a set V {\displaystyle...

multigraph may connect the same two vertices. Simplicial sets should not be confused with abstract simplicial complexes, which generalize simple undirected graphs...

algebraic topology and topological data analysis, the Čech complex is an abstract simplicial complex constructed from a point cloud in any metric space which...

refinement) of a simplicial complex is another simplicial complex in which, intuitively, one or more simplices of the original complex have been partitioned...

another fixed simplicial complex. The problem is undecidable for complexes of dimension 5 or more.: 9–11  An abstract simplicial complex (ASC) is family...

topological space from distances in a set of points. It is an abstract simplicial complex that can be defined from any metric space M and distance δ by...