Talk:Directed set
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Why not use ≤ for the partial order? -- Miguel
Well, I want to make the real numbers into a directed set by directing them towards a number x0, and then the notation ≤ would clash with the ordinary order of the reals. Ideally, we would have a separate symbol, such as a round less-that symbol, or a less-than symbol with a tilde underneath. AxelBoldt
I extended the page to include the notion of a directed subset, that appears quite frequently in order theory. I leaft the rest as it was. In a first change I made an error that is now corrected. -- Markus (no login)
preorder and base of filters
As you allude to "(partial) orders", you could mention that a refexive and transitive relation is called a preorder.
For the type of preorder occuring here, I knew the terminology of "right filtering preorder".
Concerning limits, I knew them rather defined in terms of bases of filters instead of directed sets. Note that given a directed set A, you have canonically associated a base of filters (the set of all elements "bigger than" x, where x runs through A ; for a left filtering relation these are just the "balls of radius x"), but the converse is not true. MFH 23:15, 8 Mar 2005 (UTC)