Talk:Partial order

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A general remark for editing order theory topics: please consider using ^ and v instead of the html-special symbols ∧ and ∨.

I used to advocate html-math earlier too, but I just changed my browser, finding that it wont display them properly (orders and some arrows work, but all set-theoretic signs are broken). I also looked at other computers, and it did not work there either, so I think it is a general problem these days. The trouble is that on most browsers, you cannot even distinguish the problematic characters from each other. I switched from Mozilla to Firefox (both Linux), but the problem are the (true-type) fonts, not the browser. I checked some IEs too and they did not work correctly either. On one other IE it worked, but the symbols where ugly and way too big for the font size. My old Mozilla was perfect, but it used bitmap fonts which causes other weaknesses. The only things most browsers seem to be able to are ≤ and ≥, maybe also →, but no more.

The WikiProject Mathematics also recommends to be conservative about these issues, so it is probably a general problem.

--Markus Krötzsch 23:17, 11 March 2004 (UTC)[reply]

The Alexandrov topology can be defined for any partially ordered set. Here, a set is open iff it is upwards closed. However, there are other topologies of interest for varied types of partially ordered sets, so I doubt that it is "standard". -JB

The most common and easy to read graphical representation of partial orders is in my opinion not DAGs but Hasse diagrams. In this type of diagrams the direction of the order is implied by the relative positioning of the elements. If there is an arc from x to y and y is above x on the paper then x<=y.

Would you like to add those two bits of information? Be bold in updating pages :-) --AxelBoldt

Ok, I took the oportunity to add some other things. -JB

Thanks! Could you also explain the notion of "upwards closed subset"? --AxelBoldt

Which relation does "is a subobject of" refer to? -OJarnef — Preceding undated comment added 12:08, 16 November 2001 (UTC)[reply]

I think it probably refers to relations such as "is a subgroup of", "is a subspace of", "is a subring of" etc.; the term "object" is used in the sense of category theory here. --AxelBoldt

On the page it says "the element u of X is an upper bound for S if s≤u for ALL s in S". Thus an upper bound of S can only exist, if S is TOTALLY ordered, right? Thanks, Thomas — Preceding unsigned comment added by 145.254.221.229 (talk) 14:46, 5 November 2003 (UTC)[reply]

Not right: why should it imply that we can compare s and s' in S, just because we know u is greater than s and s'?

Charles Matthews 14:57, 5 November 2003 (UTC)[reply]

Maybe, for the starters, an example on this: consider the powerset of some set M and take the usual subset ordering. Then M is an upper bound of all elements of the powerset, but these elements are not totally ordered. OK? --Markus Krötzsch 23:17, 11 March 2004 (UTC)[reply]

In a textbook I am currently reading, "ordered set" is used as short for "totally ordered set" rather than for "partially ordered set". Is this totally idiosyncratic on the part of the author, or is "orderd set" an ambiguous term? Fritzlein 03:56, 28 January 2004 (UTC)[reply]

It is probably a little ambiguous indeed. However, in most contexts of the Wikipedia the intended meaning should be clear. If there are articles that only talk about ordered sets, without using more specific terms, then it might be a good idea to change the wording a bit. --Markus Krötzsch 23:17, 11 March 2004 (UTC)[reply]