Does floor topology on R have a countable basis?
123208
Show that the Sorgenfrey line does not have a countable basis.
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
77973
How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \lfloor\frac{\lfloor x\rfloor}{n}\rfloor=\lfloor\frac{x}{n}\rfloor$.
122506
Relation on countable sets
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
36184
Countability of disjoint intervals
153652
Countable ordinals are embeddable in the rationals $\Bbb Q$ -- proofs and their use of AC
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
156783
$\mathbb R$ has the same cardinality of any interval
39880
Cardinality of Orderings of $\mathbb{R}$
7678
Show "countable complement topology" is a topology
103769
The Cartesian product of a finite number of countable sets is countable
41047
Subspace Topology of a subset
101986
Prob. 2, Sec. 20 in Munkres' TOPOLOGY, 2nd ed: The dictionary order topology on $\mathbb{R} \times \mathbb{R}$ is metrizable.
74877
Every metric space with a countable base is separable
99478
countably infinite union of countably infinite sets is countable
136106
Is every open subset of $ \mathbb{R} $ uncountable?