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Connected Sets

  1. Jun 1, 2010 #1
    I have been asked if the following is true or false

    the intersection of two connected sets is connected ?

    I would have thought that if their intersection was empty they wouldn't be connected.

    If they were disjoint or course it would be empty.

    any ideas?
  2. jcsd
  3. Jun 1, 2010 #2


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    there are simple counter examples
  4. Jun 1, 2010 #3


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    The empty set definitely is connected. Take a look at the definition of not connected again... the partioning sets are required to be non-empty themselves (otherwise every set is disconnected). The empty set has no non-empty subsets so must be connected by default
  5. Jun 2, 2010 #4
    So are you saying that if I take two non empty connected sets ie.

    A= {1} and B={2} as singletons are connected then the intersection of (A n B ) = the empty set which is itself connected?
    Last edited: Jun 2, 2010
  6. Jun 2, 2010 #5
    So I need to find at least an non empty set to be dissconnected.
  7. Jun 2, 2010 #6


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    he is saying that the empty set is connected so that it will not serve for a counter example
  8. Jun 2, 2010 #7
    Thanks guys
  9. Jun 5, 2010 #8
    Just try to imagine two connected sets that cross over each other in two disconnected regions; it's not too difficult if you think about it e.g. take two connected subsets of a circle which cover the circle but are not the whole circle.
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