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Math Help - Basic topology question.

  1. #1
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    Basic topology question.

    Assume X is a metric space, and X = A\cup B where A and are closed subspaces. Can a boundary point of A or B be a boundary point of A\cup B ? My guess is that it can be, that a metric space can have a boundary. But if that's so, I am misunderstanding something else: the textbook problems I am working on involve continuity on closed sets, and the textbook defined continuity of f at xo requiring that for any open set in the image of f that contains f (xo) there be an open set in the domain containing x O s.t. the image of one open set be contained in the other. I don't see how to construct an open set in the domain that includes a boundary point of the domain.
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  2. #2
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    Re: Basic topology question.

    Never mind I got it. Thanks
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