Suppose X admits a family {Ur}r∈Q of nested neighbourhoods. Definef:X→[0,1] by f(x)=infQ(x). Verify the following:
(1) f(a)=0 for every a∈A.
(2)f(b)=1 for every b∈B.
(3) f(x)≤rr for any x∈¯Ur,
(4) f(x)≥r for any x∉Ur.
Adv.
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