Geoffrey Sangston

Is the example in the original post intended to be added to pi-base under this issue? Or can this issue be closed, since the suggested theorem has been added here...

This one is also still open as of today, and looks like everything is set up to add it. I would do it but it's pretty far from the objects...

I think this suggestion is not the direction pi-base has gone in, and can be closed. Is that correct?

Just going through open issues. I'll try to summarize the status of this one. The quick assessment is, based on new comments below, items 2, 3, and 5 are still...

@prabau @StevenClontz I'll modify the conclusion of the comment.

Also somewhat similar to [Telophase topology S65](https://topology.pi-base.org/spaces/S000065). I support adding it. I also support changing Telophase topology so that its definition makes it a subspace of line with two origins...

@Moniker1998 I'll have to think about that. If the examples serve equal purposes then I would guess the locally Euclidean example, but I'll see if I can come up with...

@Moniker1998 I think it's an issue too. As @prabau suggests, 'Circle with a doubled point' works for that one, as in [Everywhere doubled line](https://topology.pi-base.org/spaces/S000086). It's problematic because I'm also not...

> So according to Haelfinger-Reeb definition, each origin of the line with two origins is a "point de branchement", right? It's not just for spaces like the [branching line](https://en.wikipedia.org/wiki/Non-Hausdorff_manifold#Branching_line), which...

I'm kind of curious if there's a locally Euclidean space such that the [Hausdorff reflection](https://mathoverflow.net/questions/78175/largest-hausdorff-quotient/78200#78200) involves more than 1 step of gluing the non-separated (branch) points. Maybe one of the...