While I admire the intention of this book's author to make topology accessible earlier in someone's mathematical education, I believe that if you are at the intended level of this book, then perhaps topology is not something you should study right now. Studying abstract topological spaces without studying metric spaces or even analysis over Euclidean spaces first is doing injustice to your intuition and provides very less motivation to appreciate the need for topological abstraction. The book "Introduction to topology and modern analysis" by Simmons is perhaps a better introduction with this viewpoint in mind. Usually subjects like combinatorics and algebra also provide the necessary mathematical maturity to handle more abstract subjects like topology. And once someone is mature enough Topology by Munkres is the best introduction.