Hint 1: is compact, but is not

Hint 2: if is a homeomorphism, then is an infinite sequence in and thus it has a convergent subsequence also has a convergent subseq. in [0,1]...but it doesn't, since a sequence converges in the Sorgenfrey Line only if it converges in the euclidean

line FROM ABOVE, meaning: the sequence converges to a finite limit and there's only a finite number of elements of the seq. BELOW that limit...

Tonio