I've been studying introductory topology for a little bit now. I came across [this](https://www.youtube.com/watch?v=n8Sb29BSZcY%22this%22) video which explains open sets in a way I have never thought of. Even though the video is pretty elementary, I didn't know that open sets worked in this sense. If I were to 'imagine' moving toward the boundary of an open subset, I would just appear on the other side? Is this correct?

Is there any kind of intuitive way of thinking about the concept of an open set versus a closed set without just saying one is outlined with a dotted line versus a solid line. I ask this because I have never really understood why something like a domain is generally defined to be a set that is both open and connected. Why does it matter if it is open or closed? Is this just a formality? Or are open sets something that are special. I am curious because I would like to know if I have been thinking about open sets completely wrong.

Thanks.