Continuous Function with Open Range

Ted123 · 2011-11-09T13:07:52+00:00

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

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Ted123

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?

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CompuChip

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

Ted123

CompuChip said:

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

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