what is "Minimal Uncountable well-ordered set"? Can anyone make me understand what is "Minimal Uncountable well-ordered set" (Munkres, Topology, Example 2 of the limit point compactness section)?
I know what is Uncountablity and Well ordered set.
Thank You in Advance.

@cmi ℝ in the usual ordering is not well ordered. And if equipped with proper ordering, ℝ can be isomorphic to the "Minimal Uncountable well-ordered set" (assuming the continuum hypothesis), because under the continuum hypothesis, ℝ has the same cardinality as the "Minimal Uncountable well-ordered set", and therefore a bijection between them exists. We can then just define the ordering on ℝ based on the bijection and the ordering of the "Minimal Uncountable well-ordered set".
So the reason of ℝ (with the usual ordering) being "not well ordered minimal uncountable set" is not the reason you gave (can remove element), but the its ordering.
