Prove that $\mathbb{R}_l$ is not a second countable. ($\mathbb{R}_l$ are the real ones with the topology of the lower limit)
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
87983
Examples of Separable Spaces that are not Second-Countable
17733
$X$ second countable locally compact Hausdorff implies $C(X)$ separable?
14345
If $A\subset\mathbb{R^2}$ is countable, is $\mathbb{R^2}\setminus A$ path connected?
116377
The Sorgenfrey line ($\mathbb R$ endowed with the lower limit topology $\tau_l$) is Lindelöf
136321
Show that if $\sup\big\{\sum\lvert\, f(a)\rvert\big\}  0\}$ is countable.
34298
sequentially continuous on a non first-countable
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
16413
Proving existence of surjective $f:\mathbb{N} \rightarrow A$ implies $A$ is at most countable.
128766
Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
139176
The real line is not homeomorphic to any non-trivial product space
16649
Topological space with countable open cover $\{U_\alpha\} $ with each $U_\alpha$ second-countable, is second countable
3708
How can I prove that compact subset iff sequentially compact in second countable topological spaces?
136106
Is every open subset of $ \mathbb{R} $ uncountable?
95635
$\ell^{\infty}(\mathbb N)$ is not a separable space
121626
Every open cover of the real numbers has a countable subcover (Lindelöf's lemma)
139247
Real Analysis - Prove a set is countable