What is an Example of a Closed Set with an Empty Interior in Euclidean Space?

javi438
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Give an example of a closed set S in R^2 such that the closure of the interior of S does not equal to S (in set notation).

I have no idea where to start...any help would be nice!

Thanks!
 
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A good start would be the definitions of "closure" and "interior" of a set. Do you know, for example, of any sets that have empty interior?
 
the set S = {(x,y):x and y are rational numbers in [0,1]} has an empty interior
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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