Definitions of "topology" and "analysis" How do you define "topology" and "analysis"? I'm tempted to say that topology is the mathematics of...anything that involves limits. (Open and closed sets, continuous functions, etc...they can all be defined in terms of limits). But if that's an acceptable definition, how is "analysis" different? Are the two the same? Is one of them a proper subset of the other? Is the difference that topology is about the spaces and the points they contain, while analysis is about functions between those spaces?