Can we arrange an uncoutable amount of points on $\mathbb{R}^{2}$ so that their closure has dimension 0?
93389
Uncountable sets of Hausdorff dimension zero
158155
Is set of isolated points of S closed?
17607
Open maps which are not continuous
16517
Arcwise connected part of $\mathbb R^2$
75829
Dimension of open subsets of $R^n$
84751
How can it be possible to localize a ring at a set with zero divisors?
74764
Dimension for a closed subspace of $C[0,1]$.
38917
If point is zero-dimensional, how can it form a finite one dimensional line?
60053
Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
88595
Prob. 21, Sec. 17 in Munkres' TOPOLOGY, 2nd ed: Closure and complementation can result in at most 14 different sets
152478
Is there a homeomorphism between the $n$-dimensional cube to the $n$-dimensional simplex that doesn't create hard corners?
132382
Showing a set is nowhere dense in $C([0,1])$
93776
Bijective mapping between $\mathbb{R}^2$ and $\mathbb{R}$?
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
83842
Alternate proofs (other than diagonalization and topological nested sets) for uncountability of the reals?
84791
Is every connected metric space with at least two points uncountable?
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly