n-simplex
Noun
Meaning
n-simplex (plural n-simplexes)
(geometry) An n-dimensional simplex
Examples
A continuous map to a topological space X is frequently referred to as a singular n-simplex.
Elements The convex hull of any nonempty subset of the n+1 points that define an n-simplex is called a face of the simplex.
An (m+n+1)-simplex can be constructed as a join of an m-simplex and an n-simplex.
An (n+1)-simplex can be constructed as a join (∨ operator) of an n-simplex and a point, ( ).
Note that each facet of an n-simplex is an affine n-1-simplex, and thus the boundary of an n-simplex is an affine n-1-chain.
Probability main In probability theory, the points of the standard n-simplex in -space are the space of possible parameters (probabilities) of the categorical distribution on n+1 possible outcomes.