581: Star of Vertex in Simplicial Complex

<The previous article in this series | The table of contents of this series | The next article in this series>

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:
$V$: $\in \{\text{ the real vectors spaces }\}$
$C$: $\in \{\text{ the simplicial complexes on }V\}$
$p$: $\in Vert(C)$
$Q_p$: $=\{S_{\alpha }\in C|p\in Ver(S_{\alpha })\}$
$\ast star(p)$: $={\cup }_{S_{\alpha }\in Q_p}{S}_{\alpha }^{\circ }$
//

Conditions:
//

---

2: Natural Language Description

For any real vectors space, $V$, any simplicial complex on $V$, $C$, any vertex in $C$, $p$, and $Q_p:=\{S_{\alpha }\in C|p\in Ver(S_{\alpha })\}$, $star(p):={\cup }_{S_{\alpha }\in Q_p}{S}_{\alpha }^{\circ }$

---

References

<The previous article in this series | The table of contents of this series | The next article in this series>