- #1

- 74

- 0

Let [tex]f: D \rightarrow \mathbb{R}[/tex] be continuous.

Is there an easier function that counterexamples;

if D is closed, then f(D) is closed

than D={2n pi + 1/n: n in N}, f(x)=sin(x) ?????

Plus, these counterexamples are very similar ...but are they correct?

If D is not closed, then f(D) is not closed.

CE: D = (0, 1) and f(x) = 5

If D is not compact, then f(D) is not compact.

CE: We use same CE as above

If D is infinite, then f(D) is infinite.

CE: D = all real numbers and f(x) = 5

If D is an interval, then f(D) is an interval

CE: Use same CE as first

Is there an easier function that counterexamples;

if D is closed, then f(D) is closed

than D={2n pi + 1/n: n in N}, f(x)=sin(x) ?????

Plus, these counterexamples are very similar ...but are they correct?

If D is not closed, then f(D) is not closed.

CE: D = (0, 1) and f(x) = 5

If D is not compact, then f(D) is not compact.

CE: We use same CE as above

If D is infinite, then f(D) is infinite.

CE: D = all real numbers and f(x) = 5

If D is an interval, then f(D) is an interval

CE: Use same CE as first

Last edited: