Require Export TopologicalSpaces OrderTopology Completeness MetricSpaces.
Require Export Compactness Connectedness.
Definition RTop := OrderTopology Rle.
Definition R_metric (x y:R) : R := Rabs (y-x).

Lemma countable_union2
{X : Type}
{U V : Ensemble X} :
Countable U ->
Countable V ->
Countable (Union U V).