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Least upper bound

  1. Jul 14, 2009 #1
    I read the following:
    "If {[tex]T_i[/tex]} is a non empty family of topologies on our set X, then the least upper bound of this family is precisely the topology generated by the class [tex]\bigcup T_i[/tex]; that is, the class [tex]\bigcup T_i[/tex] is an open subbase for the least upper bound of the family {[tex]T_i[/tex]} ."

    I understand that the least upper bound L of a family of topologies is the intersection of all topologies which are stronger than each [tex]T_i[/tex] but I don't understand why [tex]\bigcup T_i[/tex] is a subbase for L.
  2. jcsd
  3. Jul 15, 2009 #2
    Then you should work on the proof of that.
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