I'm going to give a class to highschoolers about topology. I've prepared the beginning of the class where I introduce what is topology and give them different ways we use to describe spaces, but everything is described very intuitively since they are in highschool. For example, I describe compactness as can we put this space into a ball or dimension as the number of different direction we can go,...

Now I want to tell them some weird fact about topology, and maybe make them do some intuitive exercises, like that the Klein bottle has no inside or outside or the seven bridges of Königsberg problem.

So my question is do you know any topological problem or fun fact that highschooler can understand and find interesting enough that they would want to do topology ?

Edit I found a great book and wanted to share it here: intuitive topology by V.V. Prasolov

I'm going to give a class to highschoolers about topology. I've prepared the beginning of the class where I introduce what is topology and give them different ways we use to describe spaces, but everything is described very intuitively since they are in highschool. For example, I describe compactness as can we put this space into a ball or dimension as the number of different direction we can go,...

Now I want to tell them some weird and fun fact about topology, and maybe make them do some intuitive exercises, like that the Klein bottle has no inside or outside or the seven bridges of Königsberg problem.

So my question is do you know any topological problem or fun fact that highschooler can understand and find interesting enough that they would want to do topology ?

Edit I found a great book and wanted to share it here: intuitive topology by V.V. Prasolov