Help with writing research proposal about topological divisor of zero

Question

I have completed my M.Sc. and I want to do Ph.D. I am very much interested in Banach Algebras and the topic that has got my attention is Topological divisors of zero. I would like to study properties of topological divisors of zeros of commutative Banach Algebras. We may ask questions like Is the set of topological divisors of zero closed open? Also from Gelfand and Major theorem we can say that is a Banach algebra has only zero as a topological divisor of zero that that Banach Algebra must be $\mathbb C$. Now I am having so many thoughts about topological divisors of zero but I am struggling in writing the Research Proposal in a certain way. There are also Not much research papers on this topic available on internet. Now I am really confused what to do? Have I chosen a less promising topic for reasearch? Any guidance would be helpful