Guest aimouz9 Posted January 23, 2005 Share Posted January 23, 2005 I am having a difficulties finding an example of an open set U c R and a continuous function f that map R to R such that f(U) is not open. Link to comment Share on other sites More sharing options...
matt grime Posted January 24, 2005 Share Posted January 24, 2005 The image of any constant map is closed. Link to comment Share on other sites More sharing options...
Dave Posted January 24, 2005 Share Posted January 24, 2005 Why not take U as something you know is not open and then take f as the identity map? (this came right off the top of my head, don't know whether it's right or not). Link to comment Share on other sites More sharing options...
matt grime Posted January 24, 2005 Share Posted January 24, 2005 Because U is specified as open in the question.... Link to comment Share on other sites More sharing options...
Dave Posted January 24, 2005 Share Posted January 24, 2005 Ah, thought you had to pick a U as well. My mistake. Link to comment Share on other sites More sharing options...
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