View source for Vertex set of an abstract simplicial complex/Definition

<noinclude>
==Definition==
</noinclude>Let {{M|\mathcal{S} }} be a [[abstract simplicial complex]], we define the ''vertex set'' of {{M|\mathcal{S} }}, denoted as just {{M|V}} or {{M|V_\mathcal{S} }}, as follows{{rEOATJRM}}:
* {{MM|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 {{M|\mathcal{S} }}
'''Note: ''' we do not usually distinguish between {{M|v\in V_\mathcal{S} }} and {{M|\{v\}\in\mathcal{S} }}<ref name="EOATJRM"/>, they are [[notionally identified]].<noinclude>
==References==
<references/>
{{Definition|Homology Theory|Simplicial Homology Theory|Algebraic Topology}}
</noinclude>