Why the rationals do not form a countable intersection of open sets?
4518
How would one go about proving that the rationals are not the countable intersection of open sets?
136106
Is every open subset of $ \mathbb{R} $ uncountable?
44623
Closed set as a countable intersection of open sets
21892
Any open subset of $\Bbb R$ is a countable union of disjoint open intervals
13620
$\omega_2$ is a not countable union of countable sets without AC
64861
Intersection of open affines can be covered by open sets distinguished in *both*affines
86685
Example of a set $S$ that is countable, but the set of limit points is uncountable
10247
What is the minimum $ \sigma$-algebra that contains open intervals with rational endpoints
68994
Countable closed sets
107370
An open covering of $\mathbb{Q} \cap [0,1]$ that does not contain any finite subcovering
16654
Unions and Intersections of Open Sets are Open
136108
Arbitrary intersection of closed, connected subsets of a compact space connected?
6491
Not every open set in $\mathbb{R}^n$, for $n\geq2$, is a disjoint union of countable open balls.
108052
Does any connected metrizable space with more than one element have uncountably many open sets, each generating a connected subspace?
128766
Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
125233
Why is an open interval not a compact set?
148507
Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?