Vertex set of an abstract simplicial complex
From Maths
Revision as of 11:38, 19 February 2017 by Alec (Talk | contribs) (Moved definition into a subpage. That subpage had some changes too, just adding notational note to first line and a words version of the definition)
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
Contents
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]:
- [math]V_\mathcal{S}:\eq\bigcup_{A\in\{B\in\mathcal{S}\ \vert\ \vert B\vert\eq 1 \} } A[/math] - 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.
