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Ted123
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What is an example of a continuous function f:\mathbb{R}\to\mathbb{R} such that f(\mathbb{R}) is open?
Continuous Function with Open Range
- Thread starter Ted123
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A continuous function f:ℝ→ℝ that has an open range is exemplified by f(x)=x, as the entire set of real numbers ℝ is considered open in the context of real analysis. The discussion highlights that the function's output covers all real numbers, confirming that its range is indeed open. Participants emphasize the significance of understanding the properties of continuous functions and their ranges. The conversation reiterates the definition of open sets in relation to the real number line. This example effectively illustrates the concept of continuous functions with open ranges.