For any collection C of sets, let denote the union of all of the elements of C. That is, let
The pseudo-arc is defined as follows:
- Let p and q be distinct points in the plane and be a sequence of chains in the plane such that for each i,
-
- the first link of contains p and the last link contains q,
- the chain is a -chain,
- the closure of each link of is a subset of some link of, and
- the chain is crooked in .
- Let
- Then P is a pseudo-arc.
Read more about this topic: Pseudo-arc, Construction