# Does continuous extension exists under specific conditions

I was unable to solve this problem asked in my exam of Topology and need help.

True or False : Does A continuous function on $$\mathbb{Q}$$ Intersection [0, 1] can be extended to a continuous function on [0, 1] .

I couldn't think of what theorem or counterexample I should use and hence I am posting here.

• Are you asking if a continuous function $f$ on $\mathbb{Q} \cap [0,1]$ can always be extended to a continuous function on $[0,1]$, or if there are continuous functions on this domain that are not continuous on $[0,1]$? Jun 25, 2020 at 17:40
Hint: What is the simplest function you can think of that blows up at $$1/\sqrt 2?$$
• I was thinking $1/(x-1/\sqrt 2).$