I am reading a book and it stated "All index sets will be assumed to be filtered". I was wondering if someone could explain what this meant. I did a quick search on the web but I couldn't figure out exactly what the author meant. Thank you.
2026-04-11 14:50:37.1775919037
What does "index sets are filtered" mean?
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They are almost certainly talking about a directed set. This is a poset $(I, \leq)$ with the additional property that for each $x, y \in I$ there is a $z \in I$ such that $x \leq z$ and $y \leq z$. That is, each pair of elements has an upper bound.