In the post below, I attempted an easy introduction to a notable result of point-set topology, the Urysohn Metrization Theorem. I noted in passing an occasional disparity in the premise of the theory: positing that the space be regular vs. normal.
Now, just browsing around, I stumble across an explanation -- on a site for children -- -- for Australian children no less:
The first really useful metrization theorem was Urysohn's Metrization Theorem. This states that every second-countable regular Hausdorff space is metrizable. So, for example, every second-countable manifold is metrizable. (Historical note: The form of the theorem shown here was in fact proved by Tychonoff[?] in 1926. What Urysohn had shown, in a paper published posthumously in 1925, was the slightly weaker result that every second-countable normal Hausdorff space is metrizable.)
Their age, my day, we was out playing stickball.
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Okay, even stranger. Surfed some more, and was led to a page about the theorem; but the root is this site -- a middle-of-the-road, sedately Christian sort of place (much like my own home, though not my intellectual like), with dozens and dozens of homely posts, offering such sage advice as
Six ways to make people like you
1. Become genuinely interested in other people.
2. Smile.
You have to scroll quite a bit before you hit a link “mathematics notes”, which opens up a whole new room.
Back in my time, they didn’t teach us that stuff in Sunday school. Barely made it past the Tietze extension theorem.
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