Continuous Function with Open Range

Ted123 · Nov 9, 2011

What is an example of a continuous function [itex]f:\mathbb{R}\to\mathbb{R}[/itex] such that [itex]f(\mathbb{R})[/itex] is open?

CompuChip · Nov 9, 2011

Well, [itex]\mathbb{R}[/itex] is open in [itex]\mathbb{R}[/itex], right?

Ted123 · Nov 9, 2011

CompuChip said:

Well, [itex]\mathbb{R}[/itex] is open in [itex]\mathbb{R}[/itex], right?

So [itex]f(x)=x[/itex] is open

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