Guest aimouz9 Posted January 23, 2005 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.
Dave Posted January 24, 2005 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).
matt grime Posted January 24, 2005 Posted January 24, 2005 Because U is specified as open in the question....
Dave Posted January 24, 2005 Posted January 24, 2005 Ah, thought you had to pick a U as well. My mistake.
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