Prob. 13, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Every collection of disjoint open sets in a separable space is countable
107057
How to show that any separable space is CCC
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
93419
Let $\mathcal A$ be a collection of pairwise disjoint subsets of a $\sigma$-finite measure space,Show that $\mathcal A$ is at most countable.
10513
What is the significance of the term "separable" in the context of countability properties?
33207
Bases having countable subfamilies which are bases in second countable space
44974
Infinite set and countable subsets
79779
How big can a separable Hausdorff space be?
99478
countably infinite union of countably infinite sets is countable
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?
77289
Example 2, Sec. 24, in Munkres' TOPOLOGY, 2nd ed: If $X$ is a well ordered set, then $X \times [0, 1)$ is a linear continuum
53429
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
100476
Why does a Hausdorff but not countably compact space have an infinite closed discrete subset?
136094
$G_\delta$ singletons in compact Hausdorff and first countability
128118
Is the cofinite topology on a countable set first countable?
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
74877
Every metric space with a countable base is separable
17733
$X$ second countable locally compact Hausdorff implies $C(X)$ separable?