1 votes 1 votes Answer whether the following statements are True or False. $\mathbb{R}^{2} \backslash \mathbb{Q}^{2}$ is connected but not path-connected. Others tifrmaths2022 true-false + – admin asked Sep 9, 2022 edited Mar 20, 2023 by Lakshman Bhaiya admin 444 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Use the fact ::: If A is any Countable set in ℝ^2 then ℝ^2\A is path connected which further implies connected. So notice that here , ℚ^2 is countable set thus ℝ^2\ ℚ^2 is path connected. ∴ given statement is false. Pawan367 answered Oct 31, 2022 Pawan367 comment Share Follow See all 0 reply Please log in or register to add a comment.