Topology is the most general study of geometric space. It is critical here to get beyond the “popular” accounts and learn the basics from a real math book. A classic introduction is General Topology by J.L. Kelley but there are lots of equally good choices out there.
One of the reasons I like Kelley is that it has an appendix on set theory where I got my first real taste of axiomatic set theory. I posted excerpts from the appendix and the main text to several discussion groups early in the present millennium and I archived copies at the following locations:
These are raw text copies right now but I’m in the process of segmenting them for ease of study and retrieving Internet Archive links for the discussion pages no longer live on the web.
Another good text I recall on topology is Munkres. I imagine there are newer editions still in print.