This book is about the branch of mathematics called topology.But its larger purpose is to illustrate how mathematics works: The interplay between intuition on the one hand and a puremathematical formulation on the other. Thus, we develop theaxioms for a topological space, formulate definitions withinthe context of those axioms and actually prove theorems fromthe axioms. But underlying all this is our intuition abouttopology. It is this intuition that...