continuity in R^p

[new]

Let f:R^p-->R and g:R^p-->R be functions that are contious on R^p.
If we define h: R^p-->R by h(x)= min {f(x),g(x)} at each x in R^p.
How do we show that h is continous on R^p?

I find this trick because the functions are defined on R^p.
Thank you.

[HallsofIvy]

First you should note that the only place there is a "problem" is where f(x)= g(x). If f(x)< g(x) for some x, then, by the continuity of f and g (and so of f-g), there exist some neighborhood of x for which f(x)< g(x). Then the function is identically the same as f(x) on that neighborhood. Similarly if g(x)< f(x).