math homework help one problem, differential geometry

Math Problem is: If x is a path-connected topological space then x is connected. Prove that.... (ie using differential geometry and topology...) You should be prepared to 'explain' your proof in case I don't understand something, so you can't just find the answer somewhere and give it to me, I'm not interested in just the answer, I want someone to be able to explain the steps in the proof if I need explanation so I understand it also.