definition of maximal simplex in simplicial complex
Topics
About: vectors space
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
- 3: Note
Starting Context
- The reader knows a definition of simplicial complex.
- The reader knows a definition of face of affine simplex.
Target Context
- The reader will have a definition of maximal simplex in simplicial complex.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( V\): \(\in \{\text{ the real vectors spaces }\}\)
\( C\): \(\in \{\text{ the simplicial complexes on } V\}\)
\(*S_\alpha\): \(\in C\)
//
Conditions:
\(\lnot \exists S_\beta \in C (S_\alpha \in \{\text{ the proper faces of } S_\beta\})\)
//
2: Natural Language Description
For any real vectors space, \(V\), and any simplicial complex, \(C\), on \(V\), any simplex, \(S_\alpha \in C\), such that there is no simplex, \(S_\beta \in C\), such that \(S_\alpha\) is a proper face of \(S_\beta\)
3: Note
There can be multiple maximal simplexes in \(C\).
This does not seem any prevalent term: as the author did not see any corresponding term in some textbooks but the author uses the concept, the term is defined here.
