Endow the set rtimesz with the dictionary order that is
Endow the set R×Z with the dictionary order . That is, for(x, r),(x0, r0) ∈ R×Z, we have (x, r) (x0, r0) if x x0(as real numbers) or x = x0 and r r0(as integers). Prove that the order topology on R × Z is the discrete topology.
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endow the set rtimesz with the dictionary order that is forx rx0 r0 isin rtimesz we have x r x0 r0 if x x0as real
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