For $\mathbb{R}$, does every open cover have a "countable" subcover?
121626
Every open cover of the real numbers has a countable subcover (Lindelöf's lemma)
128334
Question regarding open covers in Zariski topology (distinguished opens of affine schemes are quasi-compact)
33207
Bases having countable subfamilies which are bases in second countable space
155168
Is the collection of finite subsets of $\mathbb{Z}$ countable?
48174
Are countable topological spaces second-countable?
127900
Interior of closure of open set in topological space
152927
seemingly nontrivial question about covering maps and evenly covered open sets
29626
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?
103769
The Cartesian product of a finite number of countable sets is countable
4602
Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected
44704
familly of Radially open sets in $\mathbb{R}^2$
119649
Every metrizable space with a countable dense subset has a countable basis
4111
Outer measure is countably subadditive
14345
If $A\subset\mathbb{R^2}$ is countable, is $\mathbb{R^2}\setminus A$ path connected?
21599
$(0,1)$ is an open subset of $\mathbb{R}$ but not of $\mathbb{R}^2$, when we think of $\mathbb{R}$ as the x-axis in $\mathbb{R}^2$. Prove this.
134844
Summablity and countability
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?