I’m going to take one more day, I think, preparing the Playful Math Education Blog Carnival. It’s hard work. But while you wait let me please share an older piece. In 2017 I wrote about Open Sets. These are important things, born of topology and offering us many useful tools. One of the best is that it lets us define “neighborhoods” and, along the way, “limits” and from that, “continuity”.

It was also a chance for me to finally think about one of those obvious nagging questions. There are open sets and there are closed sets. But it’s not the case that a set is *either* open or closed. A set can be not-open without being closed, and not-closed without being open. A set can even be *both* open and closed simultaneously. How can that turn out? And I learned that while “open” and “closed” are an obvious matched pair of words, they’re about describing very different traits of sets.

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## Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.
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