Moniker1998
Moniker1998
I've posted a question about it here https://math.stackexchange.com/questions/4742936/is-bings-discrete-extension-space-realcompact
I think this space is realcompact, and it would follow if we could obtain a $\sigma$-discrete network for Bing's space G. Another author claims it's possible to obtain such network...
If a result exists that says weakly $\theta$-refinable spaces of non-measurable size are realcompact, then we are done. Bing's G space is weakly $\theta$-refinable. I don't know if it's $\theta$-refinable...
Something I found is that Bing's space is countably paracompact, but not sure if that's important.
I forgot how to do this, and additionally I'm going to be off for a week, but if no one is going to write a pull request then I will...
@GeoffreySangston @prabau which example would it be better to add? The one I defined in my math.se post, the modification to a circle, or both?
Thank you, I'll wait for what @prabau has to say, and add both circle with two origins and circle with countably many origins, if no one has an issue with...
@prabau @GeoffreySangston A circle technically doesn't have an origin, so would calling it a circle with countably many origins be fine?
@GeoffreySangston feel free to
If we are going to make the change to 1.i, then we need to change all the names "the one-point compactification" to "Alexandroff one-point compactification" for all the Hausdorff spaces...