Difference between revisions of "Vertex set of an abstract simplicial complex"

Revision as of 11:34, 19 February 2017

Stub grade: E

This page is a stub

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

Let $\mathcal{S}$ be a abstract simplicial complex, we define the vertex set of $\mathcal{S}$ as follows^[1]:

$V_\mathcal{S}:\eq\bigcup_{A\in\{B\in\mathcal{S}\ \vert\ \vert B\vert\eq 1 \} } A$

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