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Is the image of an open set under a continuous function open?
From Mathematics Is A Science
Jump to navigationJump to searchQuestion: Is the image of a open set under a continuous function always open?
Answer: No.
Why: Consider the projection of a vertical line in the plane onto the $x$-axis, or simply a constant function from ${\bf R}$ to ${\bf R}$...
Also, is the image of a closed set under a continuous function closed?
