# Vertex set of an abstract simplicial complex

This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
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 [ilmath]\mathcal{S} [/ilmath] be a abstract simplicial complex, we define the vertex set of [ilmath]\mathcal{S} [/ilmath], denoted as just [ilmath]V[/ilmath] or [ilmath]V_\mathcal{S} [/ilmath], as follows[1]:

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

Note: we do not usually distinguish between [ilmath]v\in V_\mathcal{S} [/ilmath] and [ilmath]\{v\}\in\mathcal{S} [/ilmath][1], they are notionally identified.