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Here is the problem: Let ##C## be a convex disc in the plane, and ##C_1## and ##C_2## be two translates of ##C##. Prove that ##C_1## and ##C_2## are non-crossing, that is, it isn't possible that both ##C_1 - C_2## and ##C_2 - C_1## are non-connected.
Here is my question: What exactly do the terms "non-crossing" and "non-connected" mean? Are these terms coming from topology?
Here is my question: What exactly do the terms "non-crossing" and "non-connected" mean? Are these terms coming from topology?