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TIFR Mathematics 2022 | Part B | Question-1

Answer whether the following statements are True or False.

$\mathbb{R}^{2} \backslash \mathbb{Q}^{2}$ is connected but not path-connected.

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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.
Answer:

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