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Open map

  1. Feb 10, 2009 #1
    A map f: X-> Y is said to be an open map if for every open set U of X, the set f(U) is open in Y. Show that [tex]\pi[/tex]1:X x Y -> X and [tex]\pi[/tex]2: X x Y -> Y are open maps...


    I don't know where to begin with this...
    Can someone give me an idea of where to start?

    Thank You.
     
  2. jcsd
  3. Feb 10, 2009 #2

    CompuChip

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    I suppose that [itex]\pi_i[/itex] is a projection operator, for example
    [tex]\pi_1: X \times Y \to X: (x, y) \mapsto x[/tex]

    Also you need some information on the topologies. Are X and Y topological spaces and is X x Y endowed with the induced topology (i.e. defined by products of open sets in X and open sets in Y and extended to a topology)?
     
  4. Feb 12, 2009 #3
    if you carefully look at the definition of an open set in the product topology it will be clear.
     
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