Is there a non-empty subset of $\mathbb{R} $ like $A$ such that the set of accumulation points of $A$ is itself and $A\cap\mathbb{Q} = \emptyset $
12701
Perfect set without rationals
58594
Is the empty set a subset of itself?
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
4213
The set that only contains itself
18334
Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
158018
Everywhere Super Dense Subset of $\mathbb{R}$
120064
Proving that without the axiom of choice there is a set with an accumulation point that isn'tthe limit of a convergeant sequence
101669
Cardinality of the Set of all finite subset of $\mathbb{R}$
10477
Finding the closure of A=$\mathbb Q \cap [0,1]$.
20140
Example of set which contains itself
24266
Accumulation points of the set $S=\{(\frac {1} {n}, \frac {1} {m}) \space m, n \in \mathbb N\}$
7607
How to prove that $\mathbb{Q}$ is not the intersection of a countable collection of open sets.
122463
How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set?
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
7733
If A is infinite, does there have to exist a subset of A that is equivalent to A?