Publication at Faculty of Mathematics and Physics |
2009
Abstract
Infinite coproducts of Priestley spaces are rather complex compactifications of their topological sums. One encounters new combinatorial, and new topological phenomena.
If the summands are linearly ordered, there are (as it is known) no new finite combinatorial phenomena, but the topology, as compared with the standard compactification, can be dramatically different. Even in the simplest non-trivial case, namely the coproduct of increasing finite chains, the new ('free') summands, although of course linearly ordered again, are rather complicated.
We present a full description.