Applications of topology to computer science

I'd like to write a survey on the applications of Topology in Computer Science. I plan to cover the history of topological ideas in Computer Science and also highlight a few current developments. It would be extremely helpful if anyone could give input regarding any of the questions below. Are there any papers or notes that describe the chronology of the use of topology in Computer Science? What are the most important application of results in Topology to Computer Science? What are the most interesting areas of current work that use topology to gain insight into computation? Thanks!