Questions tagged [second-countable]
For questions about second-countable topological spaces, i.e., space with countable base.
4 questions from the last 30 days
2
votes
2
answers
134
views
Prob. 12, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Is a continuous image of a first- / second-countable space is first- / second-countable?
Here is Prob. 12, Sec. 30, in the book Topology by James R. Munkres, 2nd edition:
Let $f \colon X \longrightarrow Y$ be a continuous open map. Show that if $X$ satisfies the first or the second ...
- 28.6k
5
votes
0
answers
93
views
Proof that $\mathbf{Man}$ doesn't have coproducts [duplicate]
A smooth manifold is a locally Euclidean Hausdorff space which is second countable. The latter condition means that the category $\mathbf{Man}$ of smooth manifolds has countable coproducts, but it ...
- 186k
-1
votes
0
answers
68
views
Prob. 17, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Is the subspace $\mathbb{Q}^\infty$ of $\mathbb{R}^\omega$ in the box topology Lindelof? separable?
Here is Prob. 17, Sec. 30, in the book Topology by James R. Munkres, 2nd edition:
Give $\mathbb{R}^\omega$ the box topology. Let $\mathbb{Q}^\infty$ denote the subspace consisting of sequences of ...
- 28.6k
1
vote
0
answers
94
views
Prob. 8, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Is this metric space first-countable? second-countable? separable? Lindelof? [closed]
Here is Prob. 8, Sec. 30, in the book Topology by James R. Munkres, 2nd edition:
Which of our four countability axioms does $\mathbb{R}^\omega$ in the uniform topology satisfy?
Here $\mathbb{R}^\...
- 28.6k