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Subspace/induced/relative Topology Definition

  1. Feb 15, 2010 #1
    I'm having trouble understanding the definition of a Subspace/Induced/Relative Topology. The definitions I'm finding either don't define symbols well (at all).

    If I understand correctly the definition is:

    -topological space (A,[tex]\tau[/tex])
    -subset B[tex]\subset[/tex]A

    The subspace topology on B will be the intersection of B and every part of the topology of A



    ...I apologize in advance for my LATEX work.
  2. jcsd
  3. Feb 15, 2010 #2


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    That looks correct idea for the subspace topology... but there is a serious problem in your understanding of topology: you seem to be assuming there are only finitely many open sets.
  4. Feb 15, 2010 #3
    The u's are finite for illustrative purposes. I wanted to avoid using the form given by Wikipedia because it has insufficient textual explanation.

    They have this definition, but don't specify exactly what a U is:


    It seems that me that you need to say how U fits into the first topology.
  5. Feb 15, 2010 #4


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    Yes they do: they say a U is an element of [itex]\tau[/itex].

    This is standard set-builder syntax for replacement: on the right of | you introduce a variable and its domain, and on the left of the | you have a function of that variable indicating what should go into the set you're building.
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