definition of star of vertex 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
Starting Context
- The reader knows a definition of simplicial complex.
- The reader knows a definition of simplex interior of affine simplex.
- The reader knows a definition of vertex of affine simplex.
- The reader knows a definition of vertex in simplicial complex.
Target Context
- The reader will have a definition of star of vertex 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:
\( V\): \(\in \{\text{ the real vectors spaces }\}\)
\( C\): \(\in \{\text{ the simplicial complexes on } V\}\)
\( p\): \(\in Vert (C)\)
\( Q_p\): \(= \{S_\alpha \in C \vert p \in Ver (S_\alpha)\}\)
\(*star (p)\): \(= \cup_{S_\alpha \in Q_p} S_\alpha^\circ\)
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Conditions:
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2: Natural Language Description
For any real vectors space, \(V\), any simplicial complex on \(V\), \(C\), any vertex in \(C\), \(p\), and \(Q_p := \{S_\alpha \in C \vert p \in Ver (S_\alpha)\}\), \(star (p) := \cup_{S_\alpha \in Q_p} S_\alpha^\circ\)
