Question: Assume that ¿ is a continuous order relation on a connected metric space with x0 > y0 for at least one pair x0; y0 X.

Assume that ‰¿ is a continuous order relation on a connected metric space with x0 > y0 for at least one pair x0; y0 ˆˆ X.
1. Show that for any x0; y0 ˆˆ X such that x0>y0,

2. Suppose that 7 is not complete. That is, there exists x; y A X such that neither x‰¿y nor x‰¾y. Then show that

Assume that ‰¿ is a continuous order relation on a

3. Show that X connected implies that ‰¿ is complete.

(Yo) = 3(x0)U(Y%) b. (Yo) = X a.

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