Why second countable for definition of manifold?
72602
Why is important for a manifold to have countable basis?
11959
What's wrong with this argument that $[0,1]$ is countable?
123430
Can a topological manifold be non-connected and each component with different dimension?
78624
CW complexes and manifolds
19777
Defining "Countably Infinite"
73172
Is every complex (smooth) manifold a scheme?
68514
Let $M$ be a smooth manifold and let $N$ be a manifold with boundary. If $dF_{p}$ is an isomorphism, then $F\left(p\right)\in\mbox{int}M $.
40305
Hilbert space of a free particle: Countable or Uncountable?
61255
Tangent bundle : is a manifold
110691
Proving that given any two points in a connected manifold, there exists a diffeomorphism taking one to the other
155060
Confusion about definition of manifold with boundary
108687
Open subsets in a manifold as submanifold of the same dimension?
23837
Why is $\mathbb{R}/{\sim}$ not first countable at $[0]$, where $x \sim y \Leftrightarrow x = y\text{ or }x,y \in \mathbb{Z}$?
62766
Topological Manifolds & Covers
148516
Proof that $\omega^\omega$ is completely metrizable and second countable
87983
Examples of Separable Spaces that are not Second-Countable
3708
How can I prove that compact subset iff sequentially compact in second countable topological spaces?