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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?