Numerability on subset of $\mathbb{R}$ with induced topology
70543
Does an uncountable discrete subspace of the reals exist?
16649
Topological space with countable open cover $\{U_\alpha\} $ with each $U_\alpha$ second-countable, is second countable
45485
Dimension of a subset
74498
Smallest dense subset of $\mathbb{R}$
148507
Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
126463
Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic?
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
101986
Prob. 2, Sec. 20 in Munkres' TOPOLOGY, 2nd ed: The dictionary order topology on $\mathbb{R} \times \mathbb{R}$ is metrizable.
153305
Adding subsets of regular cardinals (Jech p. 226)
7678
Show "countable complement topology" is a topology
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
66272
Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
68230
The cardinality of a countable union of sets with less than continuum cardinality
106298
Prove that some topology is not metrizable
144246
Subset of $\mathbb{R}^n$ homeomorphic to $\mathbb{R}^n$