Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

$\ell^2$ with weak topology is a cosmic space #749

Closed
Moniker1998 opened this issue Sep 8, 2024 · 1 comment
Closed

$\ell^2$ with weak topology is a cosmic space #749

Moniker1998 opened this issue Sep 8, 2024 · 1 comment

Comments

@Moniker1998
Copy link
Collaborator

Moniker1998 commented Sep 8, 2024 •
edited
Loading

One of the definitions of a cosmic space is that of an image of a separable metrizable space.

Alternatively, one could add that $\ell^2$ with weak topology is an image of a space with countable network, so itself has countable network.
@Moniker1998 Moniker1998 changed the title $\ell^2$ with weak topology is hereditarily Lindelof $\ell^2$ with weak topology is hereditarily Lindelof and hereditarily separable Sep 8, 2024
@Moniker1998 Moniker1998 changed the title $\ell^2$ with weak topology is hereditarily Lindelof and hereditarily separable $\ell^2$ with weak topology has countable network Sep 8, 2024
@Moniker1998 Moniker1998 mentioned this issue Sep 8, 2024
Closed
@Moniker1998 Moniker1998 changed the title $\ell^2$ with weak topology has countable network $\ell^2$ with weak topology is a cosmic space Sep 8, 2024
@Moniker1998
Copy link
Collaborator Author

They are actually $\aleph_0$-spaces.

#751

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Assignees
No one assigned
Labels
None yet
Projects
None yet
Milestone
No milestone
Development

No branches or pull requests
1 participant
@Moniker1998