Talk:Abstract simplicial complex

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 Field:  Topology


what is it???

Tosha 20:22, 14 Jun 2004 (UTC)

Algebraic topology section[edit]

Moved back to simplicial complex because, as written, it is not about abstract simplcial complexes. A new section here on the algebraic topology of abstract simplicial complexes, without CW complexes etc., would be welcome. Zaslav 11:28, 20 March 2007 (UTC)

error in the definition?[edit]

The definition must be wrong, I don't know the correct one, but here is X under a quantor and nowhere else, what makes the statement nonsense, although formally well-formed. —Preceding unsigned comment added by (talk) 22:04, 23 May 2009 (UTC)

Yes, one of the Δ's in the definition should have been an X. I fixed it, but I also rewrote that section to be less notation-heavy: my opinion on this sort of stylistic issue is that with care one can write as precisely in English as one can in notation, but that the result is much more readable. —David Eppstein (talk) 23:46, 23 May 2009 (UTC)

Does the empty set belong to every ASC in the enumeration?[edit]

I tried to understand how the Enumeration came about; looking at the example in the linked OEIS entry:

  a(2)=6 from the antichains {}, {{}}, {{1}}, {{2}}, {{1,2}}, {{1},{2}}

this appears to contradict the claim earlier that "the empty set belongs to every abstract simplicial complex".

I'm not at all sure I've understood it correctly, but should the count actually be A000372(n)-1? Or does the "empty set belongs" claim need modifying? Hv (talk) 10:09, 6 August 2010 (UTC)

I've changed the second claim to "the empty set belongs to every non-empty abstract simplicial complex"; I believe this is the intended interpretation. However, I still would like to see an explanation of how {} and {{}} should be interpreted as distinct ASCs. Hv (talk) 09:18, 9 August 2010 (UTC)

Face of a face[edit]

Phrasing ".. every face of a face of a complex Δ is itself a face of Δ" one had to define "face of a face" before - right? (talk) 23:27, 9 May 2013 (UTC)

Well, sort of. The point is that a face of a complex is a complex. Indeed, any subset of a complex is a complex. Another way to say what the article is trying to say is to claim that "Any subset of a face is a face". Rswarbrick (talk) 01:12, 10 May 2013 (UTC)
Thanks for quick response. My ask was a pure formal one, and not well founded, as I did add 8 min later in my vanished "Ooops"-PS: .. as you have done: "a face Y is said to belong to another face X if Y ⊂ X" - no dice, sorry. (talk) 23:35, 9 May 2013 (UTC). (talk) 22:38, 19 May 2013 (UTC)

Geometric realization[edit]

Now think of [0,1]^S as the direct limit of [0,1]^A where A ranges over finite subsets of S

It rather looks like an inverse limit. — Preceding unsigned comment added by (talk) 15:46, 24 April 2014 (UTC)

I'm also reading this for the first time ever, but direct limit seems more appropriate, since the subsets are subsets of the same set, the (direct) limit; whereas, the inverse limit suggests that the set is the product of its subsets, which seems awkward. Hard to tell if it matters much; the article is written in a sketchy survey kind of way, without spelling out much detail. (talk) 16:14, 10 November 2015 (UTC)

WTF is up with the picture.[edit]

The picture shows a "geometric representation" of an ASC that isn't a SC. However it is known (and easy to prove, and done in one of the references) that every FINITE ASC has a geometric realisation. So my question is this:

  • Do you have a picture that uses the words "geometric representation" (which it doesn't define anywhere) just to fuck with people (relying on "we said representation not realisation so GTFO noob" as a get-out clause) or is there actually a point to the example picture? (talk) 00:53, 9 May 2016 (UTC)