Current location - Training Enrollment Network - Mathematics courses - Compactness and compactness of bounded closed set sequence in mathematical analysis
Compactness and compactness of bounded closed set sequence in mathematical analysis
The key is to transform binary functions on two closed sets into univariate functions on compact sets.

Let a be a compact set, then you can define f: a->; R, f(x)=inf|x-Y|, Y∈B, and verify that d(A, B)=inf f(x)=min f(x).

It is not difficult to give an example, but you must find an unbounded closed set.

A={(x,y):x & gt; 0,y & gt= 1/x}

B={(x,y):x & gt; 0,y & lt=- 1/x}

d(A,B)=0