p44
By Urysohn's lemma, there exists f belongs to Cc(X) s.t. f(x)=1 on K1, f(x)=0 on K2....
comment:
One should noted a property of Hausdorff space, disjointed compact sets of a Hausdorff space is always separated, which means for K1 and K2, there are open sets V1 and V2 that K1 included by V1, K2 included by V2 and V1 and V2 has no common points. Then Urysohn's lemma can be applied and the preceding conclusion can be drawn.
further comment:
This book should be read in parallel with Halmos' book and an introductory topology textbook.
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