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Math Help - Showing that a given set is a basis for X x Y.

  1. #1
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    Showing that a given set is a basis for X x Y.

    Show that if \mathcal{B} is a basis for X and \mathcal{G} is a basis for Y, then \mathcal{B} \times \mathcal{G} = \{B \times G|B \in \mathcal{B}, G \in \mathcal{G}\} is a basis for X \times Y.

    Any help would be appreciated.
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  2. #2
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    This question is too vague to answer.
    The basis for what?
    Are we in a vector space, a metric space, or a general topological space?
    You must be very specific in asking a question. We are not mind-reader.
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  3. #3
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    Sorry, we are in a general topological space.
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  4. #4
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    Well O.K.
    What defines a basis?
    Does  \mathcal{B} \times \mathcal{G} constitute a basis?
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