Is this quotient space first countable?
23837
Why is $\mathbb{R}/{\sim}$ not first countable at $[0]$, where $x \sim y \Leftrightarrow x = y\text{ or }x,y \in \mathbb{Z}$?
28422
What's an intuitive way of looking at quotient spaces?
27937
Cartesian Product of Two Countable Sets is Countable
36184
Countability of disjoint intervals
16649
Topological space with countable open cover $\{U_\alpha\} $ with each $U_\alpha$ second-countable, is second countable
127166
Specific example of a space that is separable but not second countable.
89264
Connectedness in the Quotient Space
9021
An infinite subset of a countable set is countable
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
55978
Prove that for every countable ordinal $\alpha$, $\alpha\times[0,1)$ is order isomoprhic to $[0,1)$
87983
Examples of Separable Spaces that are not Second-Countable
63276
Is an arbitrary union of a chain of countable sets countable?
130361
Basis for a topology with a countable number of sets
74720
Is every set of measure zero countable?
152547
Is the sum of all natural numbers countable?
81873
Is $(X,\mathcal T)$ necessarily an indiscrete space?
19297
Is the cofinite topology on an uncountable set first countable?