pi-base
Bing's space is realcompact?
I think the property was very successfully introduced to pi-base.
In #372 I mention ~~two spaces~~ a space in which it still needs to be verified. Those are Bing's space ~~and Open long ray~~. Bing's space isn't compact, so equivalently we should verify if Bing's space is pseudocompact.
For now I don't know if this space is realcompact.
One thing to notice that $f:X\to 2^{2^\mathbb{R}}$ is a continuous bijection. However, I'm not sure if $2^{2^\mathbb{R}}$ is hereditarily realcompact.
My bad, pseudocompactness changes nothing in terms of realcompactness, so we still don't know.
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 for Bing's space H (which is almost the same), so this reinforces me. Sadly that author doesn't give 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 i.e. submetacompact.
Something I found is that Bing's space is countably paracompact, but not sure if that's important.