I Trying to understand terms in a problem

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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?
 

Math_QED

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Crossing is defined in your problem.

Connectedness is indeed a term from topology. A topological space ##(X, \mathcal{T})## is connected if the only clopen (= both closed and open) sets are ##\emptyset## and ##X##. Or equivalently, ##X## is not a disjoint union of two (non-trivial) open sets.
 
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So as someone who has a limited understanding of topology, what would be a hint or a first step for this?
 

Math_QED

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So as someone who has a limited understanding of topology, what would be a hint or a first step for this?
How does your book define disk?
 
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A convex disc is any compact, convex set with non-empty interior
 

Math_QED

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Any hints? I feel for someones who knows topology this would be an easy problem
It isn't an easy problem. I can't find a quick proof for your statement. Maybe ask to the person who assigned you this problem. Good luck.
 

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