Cool stuff in Metric spaces and topology.

I am doing a reading project on metric and topological spaces.

I wish to write a good paper/report at the end of this project talking about some cool topic.

Guys, please recommend something. (must be something specific. eg: metrization theroms, countable connected Hausdorff spaces etc. Can be anything loosely related to topological and metric spaces)

Also, Will I be able to do anything slightly original? I read about a guy who did some OG work on proximity spaces for his Bachelor thesis. Do you know some accessible topics like this?