Pseudo-arc - Construction - Pseudo-arc

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,
  1. the first link of contains p and the last link contains q,
  2. the chain is a -chain,
  3. the closure of each link of is a subset of some link of, and
  4. the chain is crooked in .
Let
Then P is a pseudo-arc.

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