Vertex set of an abstract simplicial complex

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See Abstract simplicial complex, same stuff. Needs another reference. See what Books:Combinatorial Algebraic Topology - Dmitry Kozlov has to say. Alec (talk) 11:34, 19 February 2017 (UTC)

Warning: not to be confused with the vertex scheme of an abstract simplicial complex

Definition

Let $\mathcal{S}$ be a abstract simplicial complex, we define the vertex set of $\mathcal{S}$, denoted as just $V$ or $V_\mathcal{S}$, as follows:

• $$V_\mathcal{S}:\eq\bigcup_{A\in\{B\in\mathcal{S}\ \vert\ \vert B\vert\eq 1 \} } A$$ - the union of all one-point sets in $\mathcal{S}$

Note: we do not usually distinguish between $v\in V_\mathcal{S}$ and $\{v\}\in\mathcal{S}$, they are notionally identified.

See next

• Vertex scheme