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If f: R^n --> R is continuous on R^n and alpha<beta, show that the set {x in R^n: alpha <= f(x) <= beta} is closed in R^n.

Let f be continuous on R^2 to R^n. Define the function g1,g2 on R to R^n by g1(t)=f(t,0) and g2(t)=f(0,t). Show that g1 and g2 are continuous.

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Continuous quality is explored.

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