Context
Currently, I am a high school student working towards completing my IB diploma program, which includes a component called the Extended Essay. The extended essay is an in-depth study of a focused topic chosen from the list of available Diploma Programme subjects for the session in question. Some of which include Mathematics, Physics, History, etc. For my Extended Essay, I have chosen to conduct an in-depth study on the Banach fixed-point theorem and its application to digital image compression. I have already conducted significant research on this topic and have reached the halfway point in my draft.
Here are some of the main sources which I have been consulting:
The problem
However, I am facing challenges in progressing with my writing, particularly when it comes to discussing the mathematics involved in image compression. My research indicates that I need to understand digital topology to properly address the mathematical aspects. Unfortunately, I have never studied Topology before, and with less than a month remaining before the draft essay is due, I find myself in a difficult situation.
After reviewing the wikipedia article and other sources on Digital Topology, it seems like this knowledge may be essential for my essay. Nevertheless, I am open to suggestions and wondering if anyone has alternative ideas that might be easier to pursue. I would greatly appreciate any insights or suggestions you can share.