How can I explain topology to my grandmother? I was recently look at a post on tex.stackexchange about explaining $\LaTeX$ to the OP's grandmother. I was wondering, could the same thing be done for topology? Except in this case the "grandmother" is me. I have not fully understood the gist of topology and its capabilities. To my understanding, topology is the study of spaces but how does that translate into equations and variables? Anything would be helpful. Thanks

Topology, aka "rubber-sheet geometry", is when a teacup is identical to a donut but there is no way a teacup could ever be like this.

Topologists worry a lot about odd rings and bottles, some of them are quite concerned by knots while others try to comb hairy balls. All in all, these are rather strange characters...