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A simplicial 3-complex. In mathematics, a simplicial complex is a structured set composed of points, line segments, triangles, and their n-dimensional counterparts, called simplices, such that all the faces and intersections of the elements are also included in the set (see illustration).
Dialect – Any of the languages of the Philippines other than Tagalog (Original meaning: a variety of a standard language) Double-deck — A bunk bed. (Original meaning: something that has two decks or levels one above the other, usually a bus or tram). Duster [28] — A loose dress wore in (and near) one’s house. (Original meaning: a ...
In topology and combinatorics, it is common to "glue together" simplices to form a simplicial complex. The geometric simplex and simplicial complex should not be confused with the abstract simplicial complex, in which a simplex is simply a finite set and the complex is a family of such sets that is closed under taking subsets.
A simplicial map : is said to be a simplicial approximation of if and only if each is mapped by onto the support of () in . If such an approximation exists, one can construct a homotopy H {\displaystyle H} transforming f {\displaystyle f} into g {\displaystyle g} by defining it on each simplex; there it always exists, because simplices are ...
This can be achieved in a greedy way by iteratively removing from the simplicial complex the highest order simplexes until the simplicial complex is empty. We then need to label each vertex from 1 to | V | {\displaystyle \left\vert V\right\vert } and associate each simplex with its corresponding "word", that is the ordered list of its vertices ...
Simplicial homology is defined by a simple recipe for any abstract simplicial complex. It is a remarkable fact that simplicial homology only depends on the associated topological space. [2]: sec.8.6 As a result, it gives a computable way to distinguish one space from another.
This is a list of acronyms in the Philippines. [1] They are widely used in different sectors of Philippine society. Often acronyms are utilized to shorten the name of an institution or a company.
In mathematics, a simplicial set is a sequence of sets with internal order structure (abstract simplices) and maps between them. Simplicial sets are higher-dimensional generalizations of directed graphs. Every simplicial set gives rise to a "nice" topological space, known as its geometric realization.