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Unformatted text preview: R be generated by the basis B = { B : B = [ a,b ) , a.b ∈ Q } . 1 Determine the clouser of two sets A = (1 , √ 2) and B = ( √ 2 , 4). Problem 8. Let X and Y be two odered setsin the order topology. Show that if a map f : X → Y is bijective and order preserving then it is a homeomorphism. Problem 9. Let a function f : R → R be continuous from the right. Show that f is continuous as afunctio from R , with stabndard topology, to R with lower limit topology. Problem 10. Let X and Y be topological spaces and A ⊂ X be subspaces of X . Let Y be Hausdorﬀ. Show that if a continuous function f : A → Y may be extended to a continuous function g : ¯ A → Y , then g is uniquely determined by f . 2...
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 Spring '11
 sdd
 Math, Logic, Topology, Sets, Topological space, Hausdorf

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