580: Vertex in Simplicial Complex

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definition of vertex in simplicial complex

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Topics

About: vectors space

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Natural Language Description

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Starting Context

• The reader knows a definition of simplicial complex.
• The reader knows a definition of vertex of affine simplex.

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Target Context

• The reader will have a definition of vertex in simplicial complex.

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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.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$V$: $\in \{\text{ the real vectors spaces }\}$
$C$: $\in \{\text{ the simplicial complexes on }V\}$
$\ast p$: $\in Vert(S_{\alpha })$ for any $S_{\alpha }\in C$
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Conditions:
//

The set of the vertexes in $C$ is denoted as $Vert(C)$.

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2: Natural Language Description

For any real vectors space, $V$, and any simplicial complex on $V$, $C$, any vertex, $p\in Vert(S_{\alpha })$ for any $S_{\alpha }\in C$

The set of the vertexes in $C$ is denoted as $Vert(C)$.

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References

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