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Apr 25, 2013 at 19:09 comment added Adam Przeździecki Yes Ramiro - chain is any linearly ordered subset. I was misled by a previous answer (already deleted) which assumed well ordering of the subspaces.
Apr 25, 2013 at 13:37 comment added Ramiro de la Vega Typically a subset of a partially ordered set is a chain if any two elements are comparable (i.e. it is linearly ordered). Inside any chain you can always find a cofinal well-ordered chain, but that´s another story.
Apr 25, 2013 at 9:46 history answered Adam Przeździecki CC BY-SA 3.0