Table of Contents
14 relations: Abstract simplicial complex, Algebraic topology, Čech cohomology, Computational geometry, Empty set, Intersection (set theory), Metric space, Nerve complex, Offset filtration, Simplicial complex, Simplicial homology, Topological data analysis, Topology, Vietoris–Rips complex.
Abstract simplicial complex
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 subsets, i.e., every subset of a set in the family is also in the family. Čech complex and abstract simplicial complex are algebraic topology.
See Čech complex and Abstract simplicial complex
Algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.
See Čech complex and Algebraic topology
Čech cohomology
In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space.
See Čech complex and Čech cohomology
Computational geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.
See Čech complex and Computational geometry
Empty set
In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
See Čech complex and Empty set
Intersection (set theory)
In set theory, the intersection of two sets A and B, denoted by A \cap B, is the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A.
See Čech complex and Intersection (set theory)
Metric space
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points.
See Čech complex and Metric space
Nerve complex
In topology, the nerve complex of a set family is an abstract complex that records the pattern of intersections between the sets in the family.
See Čech complex and Nerve complex
Offset filtration
The offset filtration (also called the "union-of-balls" or "union-of-disks" filtration) is a growing sequence of metric balls used to detect the size and scale of topological features of a data set.
See Čech complex and Offset filtration
Simplicial complex
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration). Čech complex and simplicial complex are algebraic topology.
See Čech complex and Simplicial complex
Simplicial homology
In algebraic topology, simplicial homology is the sequence of homology groups of a simplicial complex.
See Čech complex and Simplicial homology
Topological data analysis
In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology.
See Čech complex and Topological data analysis
Topology
Topology (from the Greek words, and) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.
Vietoris–Rips complex
In topology, the Vietoris–Rips complex, also called the Vietoris complex or Rips complex, is a way of forming a topological space from distances in a set of points. Čech complex and Vietoris–Rips complex are algebraic topology.
See Čech complex and Vietoris–Rips complex
References
Also known as Cech complex.