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Class 9 Homework-

Suppose X admits a family {Ur}rQ of nested neighbourhoods. Definef:X[0,1] by f(x)=infQ(x). Verify the following:

(1) f(a)=0 for every aA.

(2)f(b)=1 for every bB.

(3) f(x)rr for any x¯Ur,

(4) f(x)r for any xUr.




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