[Kyrie]

Actually, I think my neighborhood basis does have a privileged position: it is the maximal neighborhood basis of +infinity consisting of connected opens.

In that case, are you not (as I suggested earlier) in essence building your case on connectedness?

Your knowledge of math is...substantial. I work with several people who have master's degrees (math) who have nearly no knowledge of set theory, model theory, etc. Unfortunately, my own knowledge is now out of date and out of practice...execpt for the basics :-(

But one more. Did you remember which "paradox" involving volumes arises from AC?

It's been fun!

[Virginia-American]

Did you remember which "paradox" involving volumes arises from AC?

Banach-Tarski - you can divide a solid sphere into five non-measurable sets and reassemble them as two spheres.